4. 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.

6. 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.

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

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

9. 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:

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

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

17. Eq 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.

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

19. Eq: 28
Set Eq 28 and 33 equal

21. Chapter 15

23. ( ) 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 ( )

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

26. 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