A baby bounces up and down in her crib. Her mass is 13.0 kg, and the crib mattress can be modeled as a light spring with force constant 788 N/m. (a) The baby soon learns to bounce with maximum amplitude and minimum effort by bending her knees at what frequency? Hz (b) If she were to use the mattress as a trampoline-losing contact with it for part of each cycle-what minimum amplitude of oscillation does she require? cm

a) 0.804second

b) 0.162m

Explanation:

In simple harmonic motion;

Period T = 2π√m/k

Where m is the mass of the object

K is the force constant

Given:

M = 13.0kg

K = 788N/m

T = 2π√13/788

T = 2π√0.0165

T = 2π*0.128

T = 0.804second

Frequency is the reciprocal of the period. F = 1/T

F = 1/0.804

F = 1.244Hertz

b) To get the amplitude x, we will use the relationship F = kx where F is the force exerted by the baby of mass 13kg

x = F/k

Since F = mg

x = mg/k

Assume g = 9.81m/s²

x = (13*9.81) / 788

x = 127.53/788

x = 0.162m

The minimum amplitude that she requires is 0.162m