An object of mass m = 0 . 25 kg has a horizontal spring attached to its left sid

Question

An object of mass m = 0.25kg has a horizontal spring attached to its left side, and slides along a frictionless surface. The spring constant is k = 0.4N/m. At t = 0s, the object is displaced 0.1m to the right of its equilibrium position. Its initial velocity is 0.4m/s, toward the right.

a) What is the period T of the motion?

b) What is the angular frequency w?

c) What is the frequency n?

d) What is the total energy E?

e) What is the amplitude A of the motion? (careful!)

f) What is the phase angle f?

g) What is the maximum velocity vmax? (careful!)

h) What is the maximum acceleration amax?

i) What are the position, velocity, and acceleration at t = p/8 s?

Explanation / Answer

a) T = 2*pi*sqrt(m/k) = 4.965 s
b)f = 1/T = 0.2 Hz
w = 2*pi*f = 1.265 rad/s

c)f = 1/T = 0.2 Hz

d) E=0.5*k*x^2 + 0.5*m*v^2 = 0.022 J

e)0.5*k*A^2 = E ===> A = sqrt(2*E/k) = 0.33m

f)
g) 0.5*m*Vmax^2 = E ===> Vmax = sqrt(2*E/m) =

h)F = k*A ==> a = k*A/m = 0.42 m/s

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