Simple harmonic motion Definition and 910 Threads

Hi everybody, I'm writing an exploration on the mathematics of simple harmonic motion and I stumbled across something I fail to understand in one of my resources (http://tutorial.math.lamar.edu/Classes/DE/Vibrations.aspx). In the example the author uses toward the end of the resource, the...

Homework Statement Which of these forces could result in simple harmonic motion F(x)=−9(x−7)3 F(x)=−9x+7 F(x)=−9x3 F(x)=−9x F(x)=9x F(x)=9x3 9x3 is 9x^3, same with itsopposite Homework Equations F=kx, the definition of shm The Attempt at a Solution I figured -9x and 9x were the only...

Homework Statement Prove that: x=8sin2t+6cos2t is undergoing S.H.M. (Not too sure about how to prove for solution.) Homework Equations Solution for S.H.M. x=asin(nt+α) is \frac{d^{2}x}{dy^{2}}=-n^2xThe Attempt at a Solution...

Homework Statement A mass on a spring has an angular oscillation frequency of 2.56 rad/s. The spring constant is 27.2 N/m, and the system's kinetic energy is 4.16 J when t = 1.56 s. What is the oscillation amplitude? Assume that the mass is at its equilibrium position when t = 0.a. 63.1 cm b...

Homework Statement What length must the pendulum be changed to in order to show the correct time? L=0.5m After 12hours the clock is behind by 30minutes. Homework Equations w=sqrt(g/L) w=2πf The Attempt at a Solution I thought if I set the frequency equal to 1Hz and solved for length it would...

Find the spring constant by timing simple harmonic motion. I have done a Hooke's law experiment already and found out about initial tension. What I learned was: force ≠ spring constant x displacement force = initial tension + (spring constant x displacement) So using F=kx would not give an...

Homework Statement A mass m = 750 g is connected to a spring with spring constant k = 1.5 N/m. At t = 0 the mass is set into simple harmonic motion (no damping) with the initial conditions represented by the point P in the phase space diagram at the right. **(This phase space diagram has...

Homework Statement http://i.imgur.com/u8vUv5a.jpg Find the phase constant. Homework Equations x(t)=Acos(ωt + Φ) v(t)=-Aωsin(ωt + Φ) Vmax = ωA ω=2π/T The Attempt at a Solution ω = 2π/12 = 0.5236 A = 60/0.5236 = 114.59 cm v(0) = -30 = -114.59(0.5236)sinΦ 0.5 = sinΦ Φ = π/6 and 5π/6. Which...

Homework Statement The position of a 50 g oscillating mass is given by x(t)=(2.0cm)cos(10t−π/4), where t is in s. If necessary, round your answers to three significant figures. Determine: The total energy. Homework Equations T = 2π/w T = 2π√m/k 1/2kA^2 1/2mv^2 1/2kx^2 The Attempt at a Solution...

Homework Statement I have a question about simple harmonic motion: Where it says " if we denote the ratio k/m with the symbol omega squared ... ": I know it says that they chose omega squared to make the solution simpler, but I mean, to me it doesn't really make sense. Omega is associated...

Homework Statement Which of the following is a forced frequency acting on the oscillations? I. A pendulum skims the surface of a pool of water at the lowest point of motion. II. To keep a bell ringing, a bell ringer pulls on a bell rope. III. A singer shatters a glass. Homework EquationsThe...

Homework Statement A mass m is sliding back and forth in a simple harmonic motion (SHM) with an amplitude A on a horizontal frictionless surface. At a point a distance L away from equilibrium, the speed of the plate is vL (vL is larger than zero). Homework Equations What is the period of the...

Hi pf. I have a question about an experiment. If you lie a ruler horizontally across two supports (one near each end) and then hang a weight in the middle it will undergo SHM if you pull the mass down. If you move the supports in closer it will oscillate with a higher frequency. I just wanted to...

Homework Statement three harmonic function of frequency p, 2p ,3p were added together. what is the frequency of resultant periodic function? Homework Equations X=Asin(wt) A-amplitude w-frequency X=X1+X2+X3 The Attempt at a Solution need a hint ..

Homework Statement So I have to write a report based on an experiment that I have conducted. I know that my report is connected with Simple Harmonic motion and Elastic force, but I do not know how to describe it in a more efficient/scientific way. Essentially, I am dropping a weight (constant)...

Homework Statement Write a program to simulate motion of simple harmonic oscillator. Initial conditions: Let ω = 1, x(t=0) = 1, v(t=0) = 0. Integrate over 30 seconds in intervals of 0.05s. Homework Equations δ2x / δt2 = -ω2x As set of 2 coupled ODE's; x' = v, v' = -w2x The...

*note: my previous thread will be deleted because I didn't include relevant equations + I put two unrelated problems in the same thread. 1. Homework Statement A cat bobble head doll consists of a weighted head on top of a spring. When the head hangs straight sown in equilibrium, it is observed...

Homework Statement [/B] A mass-spring system is oscillating with an amplitude of 10.0 cm. What is the speed of the mass at a location where the kinetic energy of the mass and the potential energy of the spring are equal? I want to know if it's possible to solve for just a number, that is, not...

I did an experiment at school, and the experiment SET UP that i did is basically shown in the word attachment link. http://www.schoolphysics.co.uk/age16-19/Mechanics/Statics/experiments/bending_of_a_beam.doc. I have two questions! Question 1:when i did the experiment, I found that with a...

Homework Statement Two particles oscillate in simple harmonic motion with amplitude A, about the centre of a common straight line of length 2A. Each particle has a period of 3.3 s, and their phase constants differ by π/9 rad. (Assume the lagging particle starts at +A. Also assume that the...

I know this is simple, but I don't fully understand why the motion of a piston is considered to be simple harmonic? Wouldn't the piston and connecting rod have mass?

Homework Statement A horizontal plank of mass m and length L is pivoted at one end. The plank's other end is supported by a spring of force constant k (see the figure below). The plank is displaced by a small angle θ from its horizontal equilibrium position and released. Find the angular...

Given a position vs time graph of simple harmonic motion of an object and using the equation x(t) = xo = A sin (ωt +Φ), how am I supposed to find Φ? I can easily find A and the period (T). I also know T = 2 pi / ω, so I can find ω. But I don't know x(t) and t. I tried finding random points in...

For one-dimensional simple harmonic motion, the equation of motion, which is a second-order linear ordinary differential equation with constant coefficients, could be obtained by means of Newton's second law and Hooke's law and i don't get this part which...

Homework Statement Homework Equations acceleration = -(2*pi*f)^2 * x, where f is the frequency and x is the displacement from equilibrium. The Attempt at a Solution I thought the acceleration would be greatest when the displacement from equilibrium is greatest, so at point P, but the answer...

Homework Statement http://puu.sh/cAjmp/14ba3df23a.jpg Homework Equations Acceleration at any instant: -(2*pi*f)^2 * x, where x is displacement from equilibrium and f is frequency. The Attempt at a Solution Firstly, I know it can't be D as acceleration would increase as potential energy...

Homework Statement mass "m" object is located near the origin of the coordinate system. External force was exerted on the object depending on the coordinate by the formula of Fx=-4*sin(3*pi*x). Find the short oscillation period, and the potential energy depending on the coordinate. Homework...

Homework Statement Actually this is not a problem. This is about something i couldn't understand. Homework Equations where wt equals θ The Attempt at a Solution I can understand that x=r.cosθ it is obvious. But i can't understand why Vx=-V.sin(w.t) When i take a triangle from that...

Homework Statement I solved this physics question, but I am unclear about why Amplitude was the amount the spring was stretched by (which should be the new equilibrium point), instead of the amount the person pulled the mass down by (which should be the amplitude). Can anyone help? On your...

Homework Statement http://imagizer.imageshack.us/v2/275x215q90/661/kIVMcC.png Mathematical pendulum is the part of the oscillating circuit. The system is in a constant uniform magnetic field. Oscillations is small. Find the normal modes of oscilations. Homework Equations ## \begin{cases}...

Homework Statement A simple pendulum of length =30.0cm is released from rest from an angle of θ=10.0∘ to the vertical. Assuming that the pendulum undergoes simple harmonic motion, find its maximum speed. Source: https://isaacphysics.org/questions/accuracy_shm_pendulum_num Homework Equations a)...

Homework Statement A block attached to a horizontal spring of force constant 75 N/m undergoes SHM with an amplitude of 0.15 m. If the speed of the mass is 1.7 m/s when the displacement is 0.12 m from the equilibrium position, what is the mass of the block? k = 75 N v = 1.7m/s @ 0.12m...

I've been researching on Damped Oscillation (in vibrations) for a few days for a research paper, however I couldn't find any applications. I would be very thankful if anyone can tell me about its applications.

Homework Statement Explain the shape of the velocity-displacement and acceleration-displacement graphs for an object undergoing simple harmonic motion. The graph is attached to this thread Homework Equations v = wsqrt(A^2-x^2) where w = angular frequency, A = amplitude and x = displacement...

Homework Statement Question: "The midpoint of a guitar string oscillates with an amplitude of 2.24mm with a frequency of 400Hz. Calculate: i) The maximum speed at this point ii) The maximum acceleration of the string at this point" Homework Equations Suitable formulas: x=Asin(2*pi*f*t) ...

For example, I have a pendulum with amplitude of 2m, when the pendulum is at a displacement of 2m, wouldn't the acceleration be negative as the restoring force is acting towards equilibrium? The equation I am taught is that maximum acceleration is (2*pi*frequency)^2 * amplitude, which is a...

1. A platform is executing simple harmonic motion in a vertical direction with an amplitude of 5 cm and a frequency of 10/pi vibrations per second. a block is placed on the platform at the lowest point of its path. a) at what point will the block leave the platform? b)how far will the block...

Homework Statement I am trying to derive the formula for simple harmonic motion of a mass hanging on a spring. I understand the derivation for the situation when the mass and the spring are on an horizontal table. Then I go about deriving the same formula for the situation when a mass is...

I was wondering if we can somehow use the formula Potential Energy = 1/2K(x(x=Amplitude))^2 for a pendulum if we are only given the angle of displacement? Would the problems normally just say the PE at the top of the pendulum is such and such, please find max Velocity, Or also the max...

I have learned in 1st year that the under-damped simple harmonic motion can be described by the differential equation m \frac {d^2 x} {dt^2} + b \frac {dx} {dt} + kx = 0 where m is the mass, b is the constant of linear drag and k is the spring constant But the derivation is skipped...

Is the propagation of a wave simple harmonic motion? Simple harmonic motion is defined when the restoring force is proportional to the displacement. Hooke's Law F = -kx is an example. However at my level of understanding I have not yet read about the relationship between forces and waves and...

Homework Statement Hi all! I'm slightly confused about pendulums and simple harmonic motion. In my textbook, it says that a pendulum only exhibits simple harmonic motion when the angle is small (<10 degrees). I was wondering why this is, using equations if possible. Without the math, I think...

why simple harmonic motion is projected as or compared with uniform circular motion ?

in defining the Equation of simple harmonic motion taking origin as fixed point and the line of motion as x axis. a(acceleration) = - w^2 * x. where w^2 is positive constant. what is the reason behind taking square of w as constant not just w?

Homework Statement I was told that for an object to execute SHM, the x (distance displaced from the spring) can't be greater than e . Why is this so? i can't understand. can someone explain please? Homework Equations The Attempt at a Solution

Homework Statement A wheel with moment of inertia I. A mass of M is connected to a belt and runs over the wheel with radius R and connected to a spring with a stiffness of k which is connected to the ground. Show that if the mass is pulled down with a force of F and released the system will...

Homework Statement my question is on part d, (iv), i assume this is a pendulum experiment. the equlibrium position is at 30cm. then the negative amplitude should be located at 24.0cm. the particle moved from 24.0cm to 36.0cm. the acceleration is always acted towards the equlibrium position. so...

Q: When a sound wave with a certain intensity is detected by the tympanic membrane, the amplitude of the resultant motion is 1.0 nm (1.0 x 10-9 m). If the frequency of the sound is 600 Hz, what is the maximum speed of the membrane oscillation? My answer: 1)Vmax = wA (where w= angular velocity)...

A mass m slides on a frictionless horizontal surface, connected to two springs, as shown below. If the force have constants K1 and K2 , show that the simple harmonic sliding motion has period. T= 2 Pie (Square Root X m { K1+K2/K1K2}) So far I have →From equation T= 2Pie{SquareRoot(m/k)...