Simple harmonic motion Definition and 910 Threads

The displacement, x= Acos(\varpit+\phi), repeats for every increase in 2pi. Why can't I make the above equal to Acos(\varpit+\phi + 2pi), and divide by cos. This gives \phi]=0. This is clearly wrong. Why? And how does angular frequency apply to a mass on a spring anyways, it doesn't move in a...

Homework Statement Two blocks (m = 1.22 kg and M = 8.73 kg) and a spring (k = 344 N/m) are arranged on a horizontal, frictionless surface, with m resting on top of M and the spring attached to a wall and M. The coefficient of static friction between the blocks is 0.42. Find the maximum...

Homework Statement A loudspeaker diaphragm is producing a sound for 2.5 s by moving back and forth in simple harmonic motion. The angular frequency of the motion is 7.54 x 10^4 rad/s. How many times does the diaphragm move back and forth? Homework Equations angular freq. (W for...

Homework Statement Ok here's the problem.. a little lengthy so bear with me :) (3 parts need help w/ last two) Expectant parents are thrilled to hear their unborn baby's heartbeat, revealed by an ultrasonic motion detector. Suppose the fetus's ventricular wall moves in simple harmonic...

Homework Statement A child with poor table manners is sliding his 240 g dinner plate back and forth in SHM with an amplitude of 0.110 m on a horizontal surface. At a point a distance 7.00×10−2 m away from equilibrium, the speed of the plate is 0.350 m/s 1.What is the period? 2.What...

1. Determine the value of the acceleration due to gravity on planet X if a pendulum having a length of 30.0 cm has a frequency of .70 hz on that planet? 2. Find the period of motion for a 200 gram mass vibrating on a spring having a spring constant of 4.0 n/m? 3. When a mass of 35.0 grams...

Homework Statement Well it's actually a colection of questions that I'd like to know if I've got the right end of the stick in answering; Data to work with (just making it up): Period (T) Mass (m) Radius of disk (r) Gravitational Accelaration (g) 9.81 ms-2 1) Say we have a disk...

Homework Statement A 1.08 kg block is attached to a horizontal spring with spring constant 3650 N/m. The block is at rest on a frictionless surface. A 10.6 g bullet is fired into the block, in the face opposite the spring, and sticks. What was the bullet's speed if the subsequent...

On The Student Room I saw a couple of guys looking at whether the rules for Simple Harmonic Motion at non-relativistic speeds (e.g. a = -w2y and so on) would work if the maximum velocity of the particle hits relativistic speeds. Many Thanks W101

Homework Statement An object of unknown mass M is hung from a vertical spring of unknown spring constant k, and the object is observed to be at rest when the spring has extended by 14cm. The object is then given a slight push and executes SHM. Determine the period of this oscillation...

[SOLVED] Finding the Amplitude of a spring (Simple Harmonic Motion) First post here at PF, so forgive me if I make a faux pas. I'm trying to study for an upcoming Physics test and I'm having a bit of trouble with this. Homework Statement A massless spring with spring constant 19 N/m hangs...

Homework Statement A 20 cm long (L) wrench swings on its hook with a period of 0.90s. When the wrench hangs from a spring of spring constant 360 N/m (k), it stretches the spring 3.0 cm (x). What is the wrench's moment of inertia about the hook. A diagram also shows that the centre of mass...

Homework Statement An object in SHM oscillates with a period of 4.0 s and an amplitude of 10 cm. How long does the object to move from x = 0.0 cm to x = 6.0 cm? Homework Equations x(t) = Acos(ωt +φ ) The Attempt at a Solution ω = π/2 Acosφ = 0 ⇒φ = ±π/2 Since object is moving...

Homework Statement A machine part is undergoing SHM with a frequency of 5 Hz and an amplitude of 1.8 cm. How long does it take the part to go from x=0 to x=-1.80 cm ? Homework Equations x = Acos (ωt + φ) The Attempt at a Solution 1.80 cm = 1.80 cm * cos (ωt + φ) ω = 2πf = 2π*...

Homework Statement A 300g oscillator has a speed of 95.4 cm/s when its displacement is 3.0 cm and 71.4 cm/s when it displacement is 6.0 cm. What is the oscillator's maximum speed? Homework Equations x = Acos(\omegat + \phi) v = -\omegaAsin(\omegat + \phi) vmax = \omegaA v =...

\piHi everyone, I hope you can help me out with the following question. I am mainly confused about the sign Homework Statement A block in SHM with T= 4.0 s and A=0.1 m. How long does it take the object to move from x=0 m to x= 0.06 m. Homework Equations x=Acos(wt + \phi) w=2pi/T...

An object goes through simple harmonic motion with its position described as... Homework Statement An object undergoes simple harmonic motion with its position described by x(t ) = 50sin (2piet/3) C) when is Velocity first equal to 80 D) whe nis the Velocity next equal to 80...

Homework Statement A particle is in simple harmonic motion along the x axis. The amplitude of the motion is xm. When it is at x = x1, its kinetic energy is K = 5J and its potential energy (measured with U = 0 at x = 0) is U = 3J. When it is at x = –1/2xm, the kinetic and potential energies...

Homework Statement A block attached to a spring oscillates in simple harmonic motion along the x axis. The limits of its motion are x = 10 cm and x = 50 cm and it goes from one of these extremes to the other in 0.25 s. Its amplitude and frequency are: A) 40 cm, 2 Hz B) 20 cm, 4 Hz C) 40...

Homework Statement A uniform rod of mass m and length 2L is bent into 2 straight segments about its midpoint. The angle between the 2 segments is α. The bent rod is balanced on a sharp fulcrum. Find the angular frequency for small oscillations if the rod is displaced from equilibrium and...

Homework Statement A vibrating strutural beam in a spacecraft can cause problems if the frequency of vibration is fairly high. Even if the amplitude of vibration is only a fraction of a millimeter, the acceleration can be several times greater than acceleration due to gravity. As an...

Homework Statement A pendulum of length L with a bob of mass M hangs vertically. The bob is attached to a horizontal spring that has a force constant k. When the bob is directly below the pendulum support, the spring is unstretched. (a) Derive an expression for the period of the oscillating...

1. a. Jim and Gina are swinging on adjacent swings of equal length. Jim weighs about twice as much as Gina. Who takes less time to swing back and force. I got this answer, which is that they take the same time since mass doesn't affect the period in simple harmonic motion. However, I don't get...

Homework Statement A diving board oscillates with simple harmonic mothion of frequency 3.0 cycles per second.? What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there to not lose contact with the board during oscillation. Homework...

Homework Statement Write expressions for simple harmonic motion (a) with amplitude 10 cm, frequency 5.0 Hz, and maximum displacement at t=0; and (b) with amplitude 2.5 cm, angular frequency 5.0 1/s, and maximum velocity at t=0.Homework Equations \begin{gathered} x(t) = A\cos (\omega t +...

Simple Harmonic Motion- Spring problem Homework Statement A 12.5 kg mass is suspended on a 1e^5 N/m spring. The mass oscillates up and down from the equilibrium position y(t)= Asin(wt+\phi) Find the amplitude of the oscillating mass Initial position- 4.9 cm Initial velocity= +8.64...

The period of an oscillating particle is 56 s, and its amplitude is 18 cm. At t = 0, it is at its equilibrium position. Find the distances traveled during these intervals. (a) t = 0 to t = 14 s cm (b) t = 14 s to t = 28 s cm (c) t = 0 to t = 7 s cm (d) t = 7 s to t = 14 s cm x =...

Hi everyone, this is my first post on this forum. I hope you can help and maybe one day I can help some of you ;) Homework Statement I need to determine the constants of pendulum. Θ ( in radians) and Φ. I am given the length of the pendulum, 0.30m and the initial angle of release, 0.10...

Homework Statement A simple pendulum is made from a 0.653 m-long string and a small ball attached to its free end. The ball is pulled to one side through a small angle and then released from rest. After the ball is released, how much time elapses before it attains its greatest speed...

Homework Statement A weight of mass m is placed on a string. as a result it exerts a force equal to xk that tends to reduce x, where k is the spring constand and x is the distance from the equilibrium position of the spring. 1. Confirm that x = Asin(wt+ f) is indeed a solution of...

Homework Statement A particle of mass m moves in one dimension under the action of a force given by -kx where x is the displacement of the body at time t, and k is a positive constant. Using F=ma write down a differential equation for x, and verify that its solution is x=Acos(\omegat+\phi)...

Homework Statement A 150 grams particle oscillating in SHM travels 24 cm between the two extreme points in its motion with an average speed of 60cm/s Find a) angular frequency b) the maximum force on the particle C) the maximum speed The Attempt at a Solution My first...

I have a test soon and I don't get this topic! Here are two questions I'm having trouble with: 1. A simple harmonic oscillator has total energy of E. a) Determine the kinetic and potential energies when the displacement is (1/2)A. A = amplitude. b) For what value of displacement does the...

Homework Statement Low-frequency vertical oscillations are one possible cause of motion sickness, with 0.60hz having the strongest effect. Your boat is bobbing in place at just the right frequency to cause you the maximum discomfort. Part A - How much time elapses between two waves hitting...

A mass 0.2kg attached to the lower end of a light helical spring produces an extension of 0.05m. Calculate the force constant of the spring. The mass is pulled down a further 0.02m and released. Calculate the time period of subseuent oscillations and the maximum value of the accelartion...

Sand grains rest on a horzontal plate. The plate vibrates in the vertical plane with SHM of amplitude 1.5mm at a fixed frequency with acceleration equal to free fall (9.8ms^-2). What will happen to the grains of sand when the frequency of vibration is increased? I am unsure of how to tackle...

Equation given u(t) =0.2 cos (wt) + 0.5 sin (wt), where w=3pi rad/s and displacement is in feet. Describe the same motion using amplitute/phase format. Describe the same motion using complex notation For t =0.4 sec calculate u How do you calculate u? and how do you describe the...

In graphs of SHM, it says that "identify and use relevant parameters from the following graphs" 1. displacement-time My question is, what it meant by "relevant parameters"?

I'm investigating damped oscillations using a mass held between two springs. In the experiment, I measured the spring constant using a method which now doesn't make sense. I measured it by hanging masses from ONE vertical spring and graphing the force exerted by spring (mass times 9.8)...

x=xocos(2pi t/T), where xo is the maximum amplitude of oscillation and T is the period of oscillation. Find expressions for the velocity and acceleration of a car undergoing simple harmonic motion by differentiating x. [Answer: a=–(2pi/T)^2(Xo)cos(2pi t/T).] QUESTION: If xo = 0.3 m and T...

A 1000 kg car carrying two 100 kg football players travels over a bumpy "washboard" road with the bumps spaced 3.0 m apart. The driver finds that the car bounces with a max amplitude when he drives at a speed of 5.0 m/s. The car then stops and picks up three more 100 kg passengers. By how much...

Homework Statement A spring is standing upright on a table with its bottom end fastened to the table. A block is dropped from a height of 3.0 cm above the spring. The block sticks to the top end of the spring and then oscillates with an amplitude of 10 cm. What is the oscillation frequency...

hi i ned a little help with this problem please. An object is connectedto a 100 coil spring, that is hanging from the ceiling. The spring stretches by 0,160m. What is the spring constant? Im not sure how to go about with this...is the force 100? please help. Thanks

my question is: is there a way to find the work done to a spring when the only variable given is the distance (x)?? Homework Statement For the pressure gauge, what work is done by the air on the spring? Homework Equations W = 1/2kx2 Fx = kx The Attempt at a Solution I can't...

A 780-g mass is attached to a vertical spring and lowered slowly until the mass rests at its equilibrium position 30 cm below the original length of the spring. It is then set into simple harmonic motion. (a) What is the frequency and period of the oscillation? (b) What is the maximum...

Homework Statement A particle moves with simple harmonic motion of period \frac{\pi}{2} . Initially it is 8cm from the centre of motion and moving away from the centre with a speed of 4 \sqrt{2} cm/s. Find an equation for the position of the particle in time t second.Homework Equations x =...

Homework Statement For simple harmonic motion calculate the average value of KE and PE in space and time using \frac{1}{t_2-t_1}\int^{t_2}_{t_1}{f(t)dt (and the similar version for space)The Attempt at a Solution For time I get <KE> = 1/4 kA^2, <PE> = 1/4 kA^2 which makes sense but for space...

Hi, wondering if someone could help me with the following question. A mass is hung from the lower end of a light vertical spring, whose upper end is fixed. The mass is pulled down and released and the time period of the oscillating system is measured. If the time period is 0.25s and the...

been working on this for a long time, haven't got far, keep getting a negative mass! Homework Statement A 440 g block on a frictionless surface is attached to a rather limp spring of constant k = 8.7 N/m. A second block rests on the first, and the whole system executes simple harmonic...

Homework Statement mass = 1.8kg given equation in problem x(t) = (7.40cm)cos[(4.16s^-1)t - 2.42] *when i tried solving i converted 7.40cm to 0.074m find the position of the mass at t = 1.00s Homework Equations x(t) = (7.40cm)cos[(4.16s^-1)t - 2.42] The Attempt at a Solution...