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### Fundamentals Of Physics

Book edition 10th Edition
Author(s) David Halliday
Pages 1328 pages
ISBN 9781118230718

# In the engine of a locomotive, a cylindrical piece known as a piston oscillates in SHM in a cylinder head (cylindrical chamber) with an angular frequency of 180 rev/min. Its stroke (twice the amplitude) is 0.76 m.What is its maximum speed?

Its maximum speed is 7.2 m/s.

See the step by step solution

## Step 1: The given data

• Angular frequency of oscillation, .
• Stroke of the piston = 2Maximum displacement of piston, .

## Step 2: Understanding the concept of SHM

A piston of an engine of a locomotive executes a Simple Harmonic Motion. Using the formula of the maximum velocity of a body in oscillation, we can get the speed.

Formula:

The maximum velocity of a body in oscillation, (i)

(ii)

## Step 3: Calculation of maximum speed

The first step will be to convert the angular frequency into the units of rad/s from the given rev/min.

Using the formula from equation (ii), we get the angular frequency as:

Also, the maximum displacement of the piston is given as:

For SHM, the maximum speed of oscillations using equation (i) and the given values is given by:

Hence, the value of the maximum speed is 7.2 m/s .