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Physics/Simple Harmonic Motion/Forced Oscillations and Resonance

Physics/Simple Harmonic Motion/Forced Oscillations and Resonance

by Asif Zafar -
Number of replies: 3

A 1000 kg car carrying four 82kg people travels over a rough "washboard" dirt road with corrugations 4.0m apart, which cause the car to bounce on its spring suspension. The car bounces with maximum amplitude when its speed is 16km/h. The car now stops, and the four people get out. By how much does the car body rise on its suspension owing to decrease in mass?

The Question is the last prob asked in the chapter of SHM in HRW 6th edition

In reply to Asif Zafar

Re: Physics/Simple Harmonic Motion/Forced Oscillations and Resonance

by Manish Verma -
The weight of car's upper body+passengers is borne by the suspensions. The wheels+axles are suspended from the suspensions.

When car stops,

(1000 + 82x4)g = kx0 .......*

After 4 people get down, 1000g = kx ....#

Subtracting the equations * and #,

82x4g = k(x0-x) .....$

x0-x is asked, hence we need k.

Now, when the car is travelling on bumpy road, the suspensions provide the comfort effect or the cushion effect or the damping effect.

The oscillations are maintained by forced oscillations due to the bumps.

At resonance, the natural angular fequency can be taken to be equal to the frequency of the forced oscillations.

Time between two bumps = d/v (both d and v are given in the question)

Hence, angular frequency of forced oscillations = \(\frac {2\pi}{d/v}\)

Natural angular frequency = \(\omega=\frac {2\pi}{d/v}\)

\(k=m\omega^2\)

m = 1000 + 82x4

Now, the required variable can be obtained from equation $.
In reply to Manish Verma

Re: Physics/Simple Harmonic Motion/Forced Oscillations and Resonance

by ishaan biswas -

sir,

i hav another method please tell me if its right.

assuming that the car performs SHM (due to the spring) the disuance between the crests (4m) and the speed will give us T the time period Also T=2pi<root> (m/k)  from here k can be found out and the using Kx=mg x can be found out

In reply to Manish Verma

Re: Physics/Simple Harmonic Motion/Forced Oscillations and Resonance

by Asif Zafar -

Sir,

    Thank you very much for taking the time out to post a reply to my question! I have understood the solution perfectly.