Physics Help Please! *********Challenge of the day***********?

Question

A 200g ball attached to a spring with spring constant

2.70N/m oscillates horizontally on a frictionless table. Its velocity is 22.0cm/s when x= -5.00cm.

A) What is the amplitude of oscillation? A= ???cm

B) What is the speed of the ball when x= 3.00cm? v= ???cm/s

Loosing my last nerve on this problem, please help!!!!

Answer 1

We need to assume that the equilibrium position is x=0

Then x(t) = A sin (omega t)

x'(t) = A omega cos (omega t)

The frequency of a mass on a spring is:

omega = sqrt (k/m)

sin(omega t) = x(t) / A

cos (omega t) = sqrt (1 - sin(omega t) ^2)

= sqrt (1 - (x(t) / A)^2 )

= x'(t) / A omega

A^2 - x(t)^2 = x'(t)^2 / omega^2

A = sqrt (m x'(t)^2 / k + x(t)^2)

They give you the mass, spring constant, velocity, and position.  Plugnchug.

To get B), solve the equation above for x'(t) in terms of A (which is now known) and x(t).

x'(t) = omega^2 (A^2 - x(t)^2)

= k (A^2 - x(t)^2) / m