Question

A 300 kg wooden raft floats on a lake. When a 75 kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, the raft vibrates for a while.

Part A

What is the frequency of vibration?

Express your answer to two significant figures and include the appropriate units.

f =

Part B

What is the total energy of vibration (ignoring damping)?

Express your answer to two significant figures and include the appropriate units.

Etotal =

Answer 1

here,

mass of person, m = 75 kg

sink depth, d = 4 cm = 0.04 m

mass of woden shaft, ms = 300 kg

From newton second Law : SUM(F) = 0
this whole system will act spring mass system :
so
mg = k*d

spring constant, k = m*g/d

spring constant, k = 75*9.81/0.04

spring constant, k = 18393.75 N/m

Frequency of oscillation, f = (1/2*pi)*sqrt(k/m)

Frequency of oscillation, f = (1/2*pi)*sqrt(18393.75/75)

Frequency of oscillation, f = 24.6 Hz

Energy, E = 0.5 * k * x^2

Energy, E = 0.5 * 18393.75 * 0.04^2

Energy, E = 14.715 J