A 4 kg mass is attached to a spring which has a spring constant of 16 N/m. The spring is stretched to 5.0 cm from the equilibrium position, and released (starting with zero initial velocity). Assume there is no friction or damping. For the resulting oscillation, find the:

a) amplitude

b) period

c) maximum speed of the mass

d) magnitude of the maximum acceleration of the mass

e) position of the mass after 2 seconds

f) the general equation of motion, i.e. x(t)

b) = [k/m]^1/2 = [(16 N/m)/(4kg)]^1/2 = 2 rad/s

T = 2/ = seconds

x(t) = A cos( t + )

dx/dt = -A sin ( t + )

v_max = A

a_max = A ²

e) We have x = A cos( t + ), where here =0, since the function is at its maximum at time t=0 (starting at rest, with maximum stretch). Plugging in   t = 2s,   we have