Vibrations and Waves · Problem 1-11

The superposition of periodic motions — A.P. French

Physics — Waves · simple-harmonic-motion

Problem

A mass on the end of a spring oscillates with an amplitude of 5 cm at a frequency of 1 Hz (cycles per second). At

t = 0

the mass is at its equilibrium position (

x = 0

). (a) Find the possible equations describing the position of the mass as a function of time, in the form

x = A\cos(\omega t + \alpha)

, giving the numerical values of

A

\omega

, and

\alpha

. (b) What are the values of

x

dx/dt

, and

d^2x/dt^2

t = \frac{2}{3}

sec?