Physics Questions and Answers – Oscillations – Damped Simple Harmonic Motion

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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?
a) Velocity
b) Acceleration
c) Displacement from mean position
d) (velocity)2
View Answer

Answer: a
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.
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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
c) A
d) 0
View Answer

Answer: a
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
View Answer

Answer: c
Explanation: Energy in presence of damping forces is given by: 1/2kA2e-bt/m. This shows that kinetic energy decreases exponentially with time.
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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?
a) T
b) T/2
c) 2T
d) T/4
View Answer

Answer: b
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.

Sanfoundry Global Education & Learning Series – Physics – Class 11.

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Manish Bhojasia - Founder & CTO at Sanfoundry
Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn | Youtube | Instagram | Facebook | Twitter