Question

A particle on a spring moves in simple harmonic motion along the x axis between turning points x1 = 100 cm and x2 = 140 cm. At which is the following positions does the particle have maximum speed? (a) 100 cm (b) 110 cm (c) 120 cm (d) some other position (e) the same greatest value occurs at multiple points.

Answer 1

Answer:

(c) 120 cm

Explanation:

from the question, given that;

X1 = 100 cm

X2 = 140 cm

From the knowledge in Simple Harmonic motion (SHM), we know that the speed of a particle will be maximum at the mean point. And this mean point is the mean of two extreme points,

therefore the mean = (X1 +X2 ) / 2 = (100+140) / 2

this gives 120cm

option C is therefore the correct option

Answer 2

At 120cm, the particle on the spring will have maximum speed.

What is Speed?

This is defined as the rate of change of its position with time. In Simple Harmonic motion ,the speed of a particle is at maximum when at the mean point.

The mean = (X1 +X2 ) / 2

= (100+140) / 2

     = 120cm

This therefore makes option C  the most appropriate choice.

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