A 1.00 kg glider attached to a spring with a force constant of 25.0 N/m oscillat

Question

A 1.00 kg glider attached to a spring with a force constant of 25.0 N/m oscillates on a frictionless, horizontal air track. At t = 0, the glider is released from rest at x = -3.00 cm (that is, the spring is compressed by 3.00 cm), Find: (a) the angular frequency and the period of the glider's motion, (b) the amplitude and the phase constant, (c) the maximum values of its speed and acceleration, (d) the position, velocity, and acceleration as functions of time, (e) the total energy of the system (f) the speed of the object when it s position is 1.00 cm, and (g) the kinetic energy and the potential energy when its position s 2.00 cm.

Explanation / Answer

given, mass of slider, m = 1 kg
spring force constant, k = 25 N/m

at t = 0, x = -3 cm, v = 0

a. angular frequency = w = sqrot(k/m) = 5 rad/s
   Period, T = 2*pi/w = 1.256 s

b. Amplitude of motion = initial displacement from the equilibrium position
   A = 3 cm
   phase constant = phi
   for equaiton x = Asin(wt + phi)
   phi = -90 deg

c. Vmax = A*w = 15 cm/s
   amax = AW^2 = 75 cm/s/s

d. x(t) = 3sin(5t - 90)
   v(t) = 15cos(5t - 90)
   a(t) = -75sin(5t - 90)

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