This set of Physics Multiple Choice Questions & Answers (MCQs) focuses on “Oscillations – Damped Simple Harmonic Motion”.
1. Damping force on a spring mass system is proportional to which of the following quantities?
c) Displacement from mean position
Explanation: We know from Stoke’s law that damping force is proportional to velocity of a body. It also depends on the surface area in contact with the source of particles causing damping, like air.
2. If the restoring force on a body is given by: F = -kx -bv, then what is the expression for amplitude of motion? Let A be amplitude without damping forces
a) Ae-at, where a is some constant
b) Aeat, where a is some constant
Explanation: The given force represents damping SHM. x(t) = Ae-atcos(bt+c). The term Ae-at is the amplitude which decreases with increase in time, until eventually the particle comes to a stop.
3. What happens to the energy of a particle, in SHM, with time in the presence of damping forces?
a) Stays constant
b) Decreases linearly
c) Decreases exponentially
d) Decreases cubically
Explanation: Energy in presence of damping forces is given by: 1/2kA2e-bt/m. This shows that kinetic energy decreases exponentially with time.
4. Consider the damped SHM of a spring mass system. If the time taken for the amplitude to become half is ‘T’, what is the time taken for mechanical energy to become half?
Explanation: Amplitude = Ae-bt/2m& Energy = 1/2kA2e-bt/m. For amplitude to become half, e-bt/2m = 1/2
Or bT/2m = ln(2)
Or T = 2m ln(2)/b For energy to become half, e-bt/m = 1/2
Or t = m ln(2)/b = T/2.
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