Question

Calculate the amplitude of the motion.

Calculate the maximum speed attained by the object.

An object with mass 2.4 kg is executing simple harmonic motion, attached to a spring with spring constant 260 N/m . When the object is 0.024 m from its equilibrium position, it is moving with a speed of 0.65 m/s .

Answer 1

Mass of the object = m = 2.4 kg

Spring constant = k = 260 N/m

Initial position of the object = X = 0.024 m

Speed of the object at this position = V = 0.65 m/s

Amplitude of the motion = A

Maximum speed of the object = V_max

The total energy of the system remains conserved.

The initial total kinetic energy of the object and the potential energy of the spring is equal to the potential energy of the spring at maximum elongation (amplitude)

kX²/2 + mV²/2 = kA²/2

kX² + mV² = kA²

(260)(0.024)² + (2.4)(0.65)² = (260)A²

A = 0.0669 m

The initial total kinetic energy of the object and the potential energy of the spring is equal to the kinetic energy of the object at maximum speed.

kX²/2 + mV²/2 = mV_max²/2

kX² + mV² = mV_max²

(260)(0.024)² + (2.4)(0.65)² = (2.4)V_max²

V_max = 0.696 m/s

Amplitude of the motion = 0.0669 m

Maximum speed of the object = 0.696 m/s