Shm Definition and 489 Threads

please view the first reply, I was unable to post my attempt here for some reason.

m1 = unknown m2 = 0.05 kg x = 0.38 m T = 0.8s Tried to plug in values into the above equations: 0.8 = 2pi*sqrt(m1+0.05/k) k = ((m1+0.05)*9.8)/0.38 Got negative values for both k and m which doesn't make sense

I have only be able to write something like: 2x(2π√(l/g)) = 2π√(m/k) 2π is a constant therefore; 2x(√(l/g)) = √(m/k) You could square both sides; 2^2x(l/g) = (m/k) But now I'm lost as to how to proceed. PS- Book answer is B Thanks

For the horizontal case of SHM, we only need to consider KE and EPE. But should we also take GPE into consideration when we are dealing with a vertical case?

For part (f) Solution is I don't understand why the bit highlighted in yellow is true. Would anybody be kind enough to help.

I have successfully completed parts A, and B, however, I am confused on Part C. Here was my attempt and the answer key's attempt: My attempt: Since I correctly knew the speed after the collision, and the gravitational potential energy after the collision if I set h=0 at when it was at rest...

I am trying to solve this homogenous linear differential equation . Since it is linear, I can use the substitution . Which gives, (line 1) (line 2) (line 3) (line 4) (line 5) Which according to Morin's equals, (line 6) However, could someone please show me steps how he got from line 5 to 6...

For this problem, How did they get that formula shown? My working is, All the solutions wrote was, Many thanks!

A textbook I am using gives the basic eqn of motion of shm as follows : X = Asin(wt + €) V =Awcos(wt+€) But other textbooks and online sources are interchanging sin and cos in above equations, so which is the correct one? Or does it depend on the phase constant €?

Is simple harmonic motion also a pure translatory motion?"A rigid body moves in pure translation if each particle of the body undergoes the same displacement as every other particle in any given time interval" [Halliday and Resnick, Physics].If not,then how does shm deviate from this definition>

When given a small displacement ##x##, the equation for m is: (i) N sin θ = m.a where N is the normal force acting on the ball and θ is angle of the ball with respect to vertical. (ii) N cos θ = m.g So: $$\tan \theta = \frac a g$$ $$\frac x R = \frac{\omega^{2} x}{g} \rightarrow \omega = \sqrt...

We know that the Ug is converted to KE and Us. I thought that since the system loses energy after the collision that we shouldn't use the equation hnew= delta x + h. I thought instead that maybe the h we should use is xmax, because that's when there is maximum Ug and there is no other energy...

Hi, I have no idea what formula to use while given these values, basically, it fits no formula. Any thing could help? Many thanks in advance Correct answer is 65

Summary:: I have come across a situation where I seem to get different equations of motion for an oscillating system. Please do help me find out where I went wrong. *I am not asking how to solve the problem* I am going to consider 4 parts of the cylinder's motion, as listed below. (There is...

at the mean position of the original block, its velocity is ##V = \omega A## once the new block is dropped we can conserve momentum in the horizontal direction $$m\omega A = (2m)v$$ $$v = \frac{\omega A}{2}$$ where ##v## is the common velocity of the blocks. but if instead of conserving linear...

Solution in 2ed manual: Solution in 1ed manual: Could someone explain why the work done by friction is multiplied by 2? I get that the distance traveled by the block in one cycle is greater than ##x_f+x_i##, but why is the coefficient two?

Under the topic of simple harmonic motion comes the composition of two SHM's with the same angular frequency, different phase constants, and amplitudes in the same directions and in perpendicular directions. composition of SHM's in same direction: say a particle undergoes two SHM's described by...

From Kleppner's Intro to Mechanics (Example 4.7, wording not exact): Two identical blocks a and b each of mass m slide without friction on a straight track. They are attached by a spring with unstretched length l and spring constant k; the mass of the spring is negligible compared to the mass of...

I don't get why the total mechanical energy is not conserved in this situation. When the length of the spring reaches the maximum, the speed of the block is 0 and we have the following equation: $$E=K+U=1/2mv^2+1/2kA^2,\text{where A is the amplitude} \implies E=1/2kx_{max}^2$$ I can't see why...

I first got the velocity of the combined mass with conservation of momentum and as it was in the mean position the velocity can be written as v = wA ( w= angular frequency , A = amplitude ) as we have to take it back to natural length i put A as the initial extension but i am getting a wrong ans...

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I've got the answer for (a). It's k = 0.78 N/m. I'm having problems with (b). I know that the equation of displacement in this case should either be : x(t) = Asin(ωt + φ) or x(t) = Acos(ωt - φ) where A = amplitudeFrom what I understand, both the equation above should give the same result as...

a) λ = 4/3 by considering the energy balance as P moves from A (2a) to B (1/2a). The E.E. at A changes into a gain in gravitational potential energy + build up of E.E. at B since the spring compresses. b) a = 5/3g by considering that the mass P is in dynamic equilibrium immediately after...

Ok so here are a few multiple choice questions that I have been given to me and these are what my selected options turned out to be Do they seem right? I am rather confused on the wording of the first question? Is it asking to state the conditions of SHM for it be in SHM? I know...

So the way I have gone about it is to assume that the equilibrium position is half way between the 2 end points, hence the amplitude of this motion is 9.3/2 = 4.65 cm Therefore the displacement of the particle when it is 2cm away from one end point should be the distance between that point and...

I am reading "Coulomb and the evolution of physics and engineering in eighteenth-century France". There it is said in page 152 para 1 that "Coulomb found that within a very wide range, the torsion device oscillated in SHM". My questions are: (1) By just looking at the time period of the...

I tried taking log and then diffrentiate the standard equation for time period of a pendulum but i am not getting the correct answer

In the given problem, i can understand that after placing the two blocks in equilibrium it oscillates with an amplitude of The answer for (b) is given as To my knowledge, m2 separate from m1 when the acceleration is greater than gsinø and so they should be separating only at max displacement...

I know four different forms in which an SHM can be represented after solving the differential and taking the superposition acos(wt+Ø) asin(wt+Ø) acos(wt-Ø) asin(wt-Ø) where a- amplitude In the above image they took B as negative in order to arrive at acos(wt+e). If i already knew i wanted...

From the first part of the question, I was able to get the value of ω which will be the same for the next SHM. But, I am having difficulties solving for the amplitude as I can't find the boundary conditions required to get the amplitude.

Could I please ask for views on this question: I've answered the whole thing and agree with the answers given in the textbook. Here are those answers (where Y is the modulus of elasticity of the string = lamda in the question): Period of motion = 2 * PI * sqrt( ma/Y ) Speed passing through...

I've generally solved introductory second order differential equations the 'normal' way; that is, using the auxiliary equation, and if it is inhomogeneous looking at the complementary function as well, and so on. I know that sometimes it can be helpful to propose an ansatz and substitute it...

My workings: ##D(t) = Asin\omega t## ##v(t) = \frac{\text{dD}}{\text{dt}}=Acos(\omega t)\omega## ##v(t) =Acos(\omega t)\omega## When displacement half of amplitude, ## Asin\omega t## = 0.5##A## ## sin\omega t## = 0.5 ##v(t) =Acos(\omega t)\omega## ##v(t) =\omega (0.5Asin\omega t)cos \omega t ##...

Continuing on from the summary, the chapter has given a graphed example. We are shown a regular cosine wave with phase angle 0 and another with phase angle (-Pi/4) in order to illustrate that the second curve is shifted rightward to the regular cosine curve because of the negative value. Now, my...

Homework Statement In A spring mass system , the spring stretches 2 cm from its 's frelength when a force of 10 N is applied . This spring is stretched 10 cm from it's free length , when a body of mass m = 2 kg is attached to it and released from rest at time t = 0 . Find the A) force constant...

Homework Statement Write the equation for a particle in simple harmonic motion with amplitude a and angular frequency w considering all distances from one extreme position and time when it is at other extreme end. Homework Equations X = A sin (wt + ∆) ∆ = phase difference The Attempt at a...

I'm in trouble trying to understand the expression ##t= \frac{1}{\omega} cos^{-1}(x/A)## that comes from ##x = Acos(\omega t)##, in which ##A## is the amplitude, ##t## is time and ##x## is displacement. When ##x = 0##, ##t = \frac{\pi}{2\omega} ##, shouldn't it be 0 since there was no movement?

Homework Statement An oscillator consists of a block attached to a spring (k=400n/m). At some time t, the position (from equilibrium), velocity, and acceleration of the block are x= .100m, v= -13.6m/s, a= -123m/s^2. What is the frequency? mass of block? amplitude. Homework Equations position...

When a mass is in SHM, and is moving towards equilibrium point, its velocity starts to increase but why does acceleration decreases? What is the gradient when velocity is increasing and when it is at maximum? Thanks a lot!

Homework Statement Two rubber pads are affixed at the bottom of a box and the assembly thus formed is placed on a uniform slope of inclination 0.5 degrees. Coeff of friction is 0.60 between the pads and the plane. Two electric motors installed in the box can make the pads move back and forth...

Homework Statement Does amplitude of an oscillating spring with an attached block depend on the block's mass? Assuming the spring has spring constant 'k' and obeys Hooke's law. How would the amplitude of the oscillating spring system be affected if the mass of the block were...

Homework Statement A block of mass m having charge q placed on smooth horizontal table and is connected to a wall thorough an unstretched spring of constant k . A horizontal electric field E parallel to spring is switched on. Find the ampliture of the shm by the block. Homework Equations kx=...

The only thing I know is that phase constant tells how much a signal is shifted along the x-axis. The answer of the question is both option a and b. I am not getting it!

Hi community, I've been looking at solutions for mass spring shm (undamped for now) ie that x = Acoswt and x = Bcoswt work as solutions for dx2/dt2 = -(k/m)x and that the general solution is the sum of these that with a trig identity can be written as x = C Cos(wt - φ) where C is...

Homework Statement You are exploring a newly discovered planet. The radius of the planet is 7.20 * 107 m. You suspend a lead weight from the lower end of a light string that is 4.00 m long and has mass 0.0280 kg. You measure that it takes 0.0685 s for a transverse pulse to travel from the...

This may be a fool question, but i can't figure where does this come from. I would really appreciate if someone can help me. Thanks.

Hello, I have recently been introduced to the topic of simple harmonic motion for the first time (I'm currently an A-level physics student). I feel that I have understood the fundamental ideas behind SHM very well. However, I have one question which has been bugging me and I can't seem to find a...

Hello guys! Today I was studying SHM and I can't understand how to proof that a = -ω2Acos(ωt+φ) gives me accelaration of particle executing simple harmonic motion! If someone "build" this equation step-by-step I would be really thankfull! :)

I have the equation for simple harmonic motion ##\displaystyle \frac{d^2x}{dx^2} + k^2 x = 0##. I have a simple question. Do we need to make an assumption about the sign of ##k## before we solve this? We have that the roots satisfy ##r^2=-k^2##. So ##r=\pm i \sqrt{k^2}##. Do I need to assume...

Homework Statement My question here isn't a specific question that has been given for homework, but a more general one. For an assignment I have to 'derive an expression for the resonant frequency, ω0' for two different systems, the first for 'a mass M connected to rigid walls via two springs'...