## I. Definition

- Simple harmonic motion occurs when the force F acting on an object is directly proportional to the displacement x of the object, but in the opposite direction.
- The force is called a restoring force because it always acts on the object to return it to its equilibrium position.

## II. Hooke's law

1. It is one of the simplest type of simple harmonic motioon.

2. in reference to springs.

2. in reference to springs.

## III. Elastic potential energy of SHM

1. The energy of spring will be always be conserved.

2. The potential energy of spring is called Elastic potential energy.

2. The potential energy of spring is called Elastic potential energy.

3. Kinetic energy and Potential energy differ in motion.

## IV. Springs in wave motion

- The amplitude A is the maximum displacement from the equilibrium position.
- The period T is the time for one complete oscillation. After time T the motion repeats itself. In general x(t) = x (t + T)
- The frequency f is the number of oscillations per second. The frequency equals the reciprocal of the period. f = 1/T
- Although simple harmonic motion is not motion in a circle, it is convenient to use angular frequency by defining w = 2pf = 2p/T.

## V. SHM and uniform circular motion

1. the circular motion is also showing simple harmonic motion, as like in diagram:

2. The radius of the circle is symbolic of the displacement, x, of a spring or the amplitude, A, of a wave.

3. Since both algebraic expressions have the ratio of the Amplitude to the velocity we can set them equal to each

other. This derives the period of the spring, as shown:

3. Since both algebraic expressions have the ratio of the Amplitude to the velocity we can set them equal to each

other. This derives the period of the spring, as shown:

## VI. Pendulums

1. pendulums also, like spring, shows SHM.

## VII. Equations you will have to know

1. f= #cycles/time

2. Hooke's Law: F= -kx, U= (1/2)kx^2

3. T= time/#cycles= 1/f= 2pi(L/g)^(1/2)= 2pi(m/k)^(1/2)

2. Hooke's Law: F= -kx, U= (1/2)kx^2

3. T= time/#cycles= 1/f= 2pi(L/g)^(1/2)= 2pi(m/k)^(1/2)