Question

Problem 2 A 0.175-kg glider on a horizontal, frictionless air track is attached to a fixed ideal spring with spring constant 155 N/m. When the glider is 3.00 cm from its equilibrium point, it is moving at 0.815 m/s. (a) Find the frequency of the oscillations. (b) Find the amplitude of the motion. (c) Find the maximum speed of the glider. Hint: For (b) and (c), use the energy conservation.

Answer 1

Here,

a) for the frequency of the oscillation

frequency of oscillation = 1/(2pi) * sqrt(k/m)

frequency of oscillation = 1/(2pi) * sqrt(155/0.175)

frequency of oscillation = 4.74 Hz

b)

let the amplitude is A

Using conservation of energy

0.50 * 0.175 * 0.815^2 + 0.50 * 155 * 0.03^2 = 0.50 * 155 * A^2

solving for A

A = 0.04062 m = 4.06 cm

the amplitude of motion is 4.06 cm

c)

let the maximum speed of the glider is v

Using conservation of energy

0.50 * 0.175 * 0.815^2 + 0.50 * 155 * 0.03^2 = 0.50 * 0.175 * v^2

solving for v

v = 1.21 m/s

the maximum speed of the glider is 1.21 m/s