Simple Harmonic Motion questions

AI Thread Summary
The discussion centers on difficulties understanding simple harmonic motion (SHM) concepts and equations in preparation for an upcoming test. Key questions include determining kinetic and potential energies at specific displacements, calculating work done on a cart, and finding its frequency and velocity during oscillation. The user expresses frustration with the lack of clarity on which equations to apply and their derivations, particularly in a non-calculus high school physics context. There is a request for straightforward explanations on how to solve the posed problems without delving into complex derivations. The urgency is emphasized due to the imminent test, highlighting the need for clear guidance on SHM equations.
hadroneater
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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 kinetic energy equal the potential energy?

2. Please refer to this picture:
http://img404.imageshack.us/img404/1311/shmlh9.jpg

A cart of mass 3 kg is held between two stretched springs as shown. A force of 60N moves the cart 0.10m from its equilibrium position. It's then released and allowed to vibrate.
a) How much work was required to move the cart 0.1m?
b) Calculate the frequency of the vibration.
c) What is the velocity of the cart as it moves through the equilibrium position?

I'm not asking for you to do my hw. I just really don't understand the equations and when to use them and how they're derived.
 
Last edited by a moderator:
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Do you know the equations for a 1D oscillator? Position is derived from a simple second order differential equation. From there we just take the derivatives to obtain velocity and acceleration.

What specifically don't you understand about the equations?
 
I take high school physics, which is non-calculus.
 
Well then it's going to be hard to explain how the equations are derived. Do you know any calculus?
 
Nevermind about the deriviation. Can someone just explain to me how to solve these equations? I've been given a dozen formulae and I don't know which one to use. We just started this chapter last friday and our teacher is giving us a test on it in less than a few days because he expects us to self-teach.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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