Question

1. Define simple harmonic motion for a particle moving in a straight line.

2. Use your definition to explain how simple harmonic motion can be represented by the equation.

3. Show that the above equation is dimensionally correct.

4. A mechanical system is known to perform simple harmonic motion. What quantity must be measured in order to determine frequency for the system?

Answer 1

1. A periodic motion in which acceleration is directly proportional to displacement and opposite in direction is called simple harmonic oscillation.

2. Mathematically, a simple harmonic oscillation can be expressed as

y = a sin wt (or) y = a cos wt

3. y = a sin w t

Sin wt has no dimension. Hence we need to consider dimension of ‘a’ only, ie, y = a, L = L

4. Its period is determined.