A 171-g object on a spring oscillates left to right on a frictionless surface wi

Question

A 171-g object on a spring oscillates left to right on a frictionless surface with a frequency of 3.00 Hz and an amplitude of 12.0 cm. (a) What is the spring constant? N/m (b) If the object starts from rest at x = 12.0 cm at t = 0 and the equilibrium point is at x = 0, what equation describes its position (in centimeters) as a function of time (in seconds)? (Use the following as necessary: t.) x(t) =

Explanation / Answer

The frequency f is: f =(1/2pi)(k/m)^0.5 (a) then k = m*(2 pi f)^2 = 0.171*(6 pi)^2 = 60.69 N/m (b) x(t) = A cos( w t + phi) A is the amplitude , phi the phase. v(t) = - A w sin(wt + phi) t = 0, x = 12.0 cm ; v = 0 then sin phi = 0 ---> phi = 0 and A = 12.0 cm. w is the angular frequency , w = 2 pi f = 6 pi s^-1 x(t) = 12.0 cos(6 pi t)

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