A novelty clock has a 0.0100-kg mass object bouncing on a spring that has a force constant of 1.25 N/m. What is the maximum velocity of the object if the object bounces 3.00 cm above and below its equilibrium position? (b) How many joules of kinetic energy does the object have at its maximum velocity?

a) Maximum velocity of the object = 0.335 m/s

b) Kinetic energy at maximum velocity = 0.000563 J = 5.63 × 10⁻⁴ J

Explanation:

Given that the

K = spring's force constant = 1.25 N/m

m = 0.01 Kg

The maximum position from equilibrium = amplitude = A = 3 cm = 0.03 m

The displacement of any body experiencing this type of motion is given as

x = A cos wt

where w = angular frequency = √(k/m) = √(1.25/0.01) = 11.18 rad/s

t = time

a) velocity of motion can be obtained from the displacement

v = dx/dt

x = A cos wt

v = dx/dt = - Aw sin wt

Maximum velocity = Aw = 0.03 × 11.18 = 0.335 m/s

b) Kinetic energy = mv²/2 = 0.01 × 0.335²/2 = 0.000563 J = 5.63 × 10⁻⁴ J

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