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### Fundamentals Of Physics

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

# A block is in SHM on the end of a spring, with position given by . If , then at t = 0 what percentage of the total mechanical energy is potential energy?

Percentage of total mechanical energy that is potential energy at t = 0 is 65.5 %.

See the step by step solution

## Step 1: The given data

1. Position of the block is

## Step 2: Understanding the concept of energy

A particle in simple harmonic motion has, at any time, potential energy

First, we have to find the position and potential energy of the block, then, we have to find the total mechanical energy which equals to maximum potential energy according to the law of conservation of energy. By taking the ratio of potential energy to maximum potential energy (E), we can find the percentage of total mechanical energy which is potential energy at t=0.

Formulae:

The displacement equation of a wave, (i)

The total potential energy of a particle, (ii)

## Step 3: Calculation of mechanical energy that is potential energy

The displacement equation at t = 0 can be given as:

Here, the total mechanical energy equals to its maximum potential energy. So, total energy is given as:

Now its potential energy at t = 0 is,

Percentage of total mechanical energy is potential energy at t = 0 is,

Therefore, percentage of total mechanical energy is potential energy at t = 0 is 65.5 %