Question

A 290 kg wooden raft floats on a lake. When a 75 kg man stands on the raft, it sinks 5.0 cm deeper into the water. When he steps off, the raft vibrates for a while. What is the frequency of vibration? What is the total energy of vibration (ignoring damping)?

Answer 1

Mass of the raft, m_r= 290kg

Mass of the man, m=75 kg

Maximum Displacement, x= 5cm=0.05m

Now It is the weight of the man only which makes the raft sinks 5cm and sets into vibration.

Then Restoring Force of the vibration= Weight of the man (at equilibrium)

where k= constant of vibration

When the man steps off the raft, it is only the raft that is vibrating. Then

Time Period of vibration,

using all calculated and given number in above,

The frequency of the vibration, (ANS)

b). Total Energy of vibration,

  (ANS)