Question

A 0.540-kg object attached to a spring with a force constant of 8.00 N/m vibrates in simple harmonic motion with an amplitude of 12.6 cm. (Assume the position of the object is at the origin at t = 0.).

How do i find the maximum speed and acceleration.

Answer 1

angular freqeuncy=sqrt(spring constant/mass)=sqrt(8/0.54)=3.7 rad/sec
let position at any time t is given by

x(t)=A sin wt

then v(t)=dx/dt=aw*cos(w*t)
v max= Aw

acceleration=a(t)=dv/dt=-Aw^2*sin(w*t)