A mass is attached to the end of a spring and set into simple harmonic motion wi

Question

A mass is attached to the end of a spring and set into simple harmonic motion with an amplitude A on a horizontal frictionless surface. Determine the following in terms of only the variable A.

(a) Values of the position (in terms of A) of the oscillating mass when its speed is 80% of its maximum value. _____________ A

(b) Values of the position (in terms of A) of the oscillating mass when the elastic potential energy of the spring is 80% of the total energy of the oscillating system.

______________ A

Explanation / Answer

a) speed = 0.8V

KE = 0.5*m*0.64V^2 = 0.64*0.5kA^2 = 0.5kx^2

x = 0.8A or -0.8A

b) 0.5*k*x^2 = 0.8*0.5*kA^2

x = sqrt(0.8)*A or -sqrt(0.8)*A = -0.8944A or 0.8944A

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