Question

what is the equation describing the motion of a mass on the end of a spring which is stretched 8.8 cm from equilibrium and then released from rest, and whose period is 0.66 s ? assume that the displacement at the start of the motion is positive.

Answer 1

x = A cos ω t at t = zero, x displacement equals amplitude

x = .088 m cos ω t describes the motion

We need yet to find ω in terms of P which is given

ω = √(k / m)

P = 1 / f and f = ω / (2 π)

Thus ω = 2 π f = 2 π / P since 1 / f = P

This gives us

x = .088 m cos 2 π / .66 * t