A particle of mass 40gm experienced a damping force proportional to its velocity. If its velocity is decreased from 100cm/sec to 10cm/sec in 23 seconds, calculate (i) relaxation time (ii) damping force when its velocity is 50cm/sec (iii) the time in which its kinetic Energy is reduced to one-tenth of its initial value, (iv)thhe total distance travelled if its initial velocity is 100cm/sec.
Answers
Explanation:
Damped Harmonic Motion
Over time, the damped harmonic oscillator’s motion will be reduced to a stop.
LEARNING OBJECTIVES
Describe the time evolution of the motion of the damped harmonic oscillator
KEY TAKEAWAYS
Key Points
To describe a damped harmonic oscillator, add a velocity dependent term, bx, where b is the vicious damping coefficient.
Solve the differential equation for the equation of motion, x(t).
Depending on the values of the damping coefficient and undamped angular frequency, the results will be one of three cases: an under damped system, an over damped system, or a critically damped system.
Key Terms
Under Damped: “The condition in which damping of an oscillator causes it to return to equilibrium with the amplitude gradually decreasing to zero; system returns to equilibrium faster but overshoots and crosses the equilibrium position one or more times. “
Critically Damped: “The condition in which the damping of an oscillator causes it to return as quickly as possible to its equilibrium position without oscillating back and forth about this position. “
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