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A particle moving with simple harmonic motion starts from rest at a distance $3m$ from the center of oscillation. If the period is 2$\pi$ seconds:

a) Find the time taken to move to a point $2m$ from the origin
b) Find the velocity and acceleration at this point

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You might want to elaborate a little more about your difficulty. What happens when you try to use the standard formula? –  Gadi A May 16 '11 at 10:03

1 Answer 1

A particle moving as a simple harmonic motion is described by the equations $$x(t) = A \cos(2\pi t/T + \phi_0)$$ and $$v(t) = -\frac{2\pi A}{T} \sin(2\pi t/T + \phi_0).$$ Here, $A$ is the amplitude, $T$ the period, and $\phi_0$ a "phase-shift" of the motion.

Given your information $T=2\pi$. Additionally you have $v(0)=0$ and $x(0)=3A$. This should suffice to solve your problem.

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