Question

consider a simple harmonic oscillation with m=0.5kg, k=10N/m and amplitude A=3cm.WHat is the total energy of the oscillation,what is the maximum speed,what is the kinetic energy?

Answer 1

w = 2 pi f = sqrt (k/m)

A = 3 cm use .03 m

let x = A sin w t
then v = A w cos wt

v is maximum when cos = 1 (or -1)
so V = v maximum = Aw
that is max speed

At that point of maximum speed for example when x = 0 and t = 0 the potential energy being (1/2) k x^2 is also 0

Therefore the total energy = kinetic energy = (1/2)mV^2

Answer 2

25 J