Any motion that repeats at regular intervals is called periodic motion or harmonic motion. In mechanics and physics, simple harmonic motion is a type of periodic motion where the restoring force is directly proportional to the displacement and acts in the direction opposite to that of displacement. Such motion is a sinusoidal function of time t.

The cosine function first repeats itself when its argument (the phase) has increased by 2π rad The word phase is used to describe a specific location within given cycle of a periodic wave. The word phase is used to describe a specific location within given cycle of a periodic wave.

(sketch x versus t) (a) -xm; (b) +xm; (c) 0

Thi The particle’s acceleration is always opposite its displacement (hence the minus sign).

c (a must have the form of Eq. 15-8) k (a measure of the stiffness of the spring) is related to the mass of the block and angular frequency of the SHM:

a (F must have the form of Eq. 15-10)

(a) 5 J; (b) 2 J; (c) 5 J

Eq. 15-26 is equivalent of Eq. 15-8, this tells that angular acceleration is proportional to the angular displacement, but apposite sign, (i.e. bob moves to the right acceleration is to the left.

all tie (in Eq. 15-29,m is included in I)

Eq: 28 Set Eq 28 and 33 equal

Chapter 15

( ) x=0 is the rest point where |F1|= k1d1 |F2|= k2d2 F2 = -F1 Spring 1 and 2 pull with the same force in opposite directions: If we move the mass to a new position x: |F1|= k1(d1+x) pulls now more than |F2|= k2(d2-x) The new net Force: Fnet = |F1|-|F2|= k1(d1+x)-k2(d2-x) = -(k1+k2)x ( )

Adding phase constant will shift it to the left, subtracting will shift it to the right

where M is its mass and r is its radius The physical pendulum consists of a disk and a rod. To find the period of oscillation first calculate the moment of inertia and the distance between the center-of-mass of the disk-rod system to the pivot. A uniform disk pivoted at its center has a rotational inertia of 1/2 Mr2 where M is its mass and r is its radius The rotational inertia of rod disk system is The rod is pivoted at one end and has a rotational inertia of