SHM:
The function sin(wt) represents simple harmonic motion (SHM) because it follows the equation of motion for SHM, which is a sinusoidal function. In SHM, the restoring force is directly proportional to the displacement from the equilibrium position and acts in the opposite direction. This results in a periodic motion that can be described by a sine or cosine function.

Periodic but not simple harmonic:
The function cos(wt) represents a periodic motion but not simple harmonic motion. It is periodic because it repeats itself after a certain time interval. However, it is not simple harmonic because it does not satisfy the conditions for SHM. In SHM, the acceleration is directly proportional to the displacement, whereas in this case, the acceleration is not directly proportional to the displacement.

Period:
The period of a periodic function is the time it takes for the function to complete one full cycle. For both sin(wt) and cos(wt), the period can be determined by finding the smallest positive value of t for which the function repeats itself.

For sin(wt), the period is given by:
T = 2π/w

For cos(wt), the period is also given by:
T = 2π/w

Both functions have the same period because the coefficient of t in both cases is w. The period only depends on the angular frequency w and is independent of the specific trigonometric function used.

Explanation:
- Simple Harmonic Motion (SHM) is a type of oscillatory motion that can be described by a sinusoidal function.
- SHM occurs when the acceleration of an object is directly proportional to its displacement from the equilibrium position and acts in the opposite direction.
- The function sin(wt) represents SHM because it follows the equation of motion for SHM, which is a sinusoidal function.
- Sin(wt) has a period of 2π/w, where w is the angular frequency.
- On the other hand, the function cos(wt) represents a periodic motion but not SHM.
- Cos(wt) is periodic because it repeats itself after a certain time interval.
- The period of cos(wt) is also 2π/w, the same as sin(wt), as it depends on the angular frequency w.
- However, cos(wt) does not satisfy the conditions for SHM, as the acceleration is not directly proportional to the displacement.
- In summary, sin(wt) represents SHM, cos(wt) represents a periodic but not simple harmonic motion, and both functions have the same period of 2π/w.

Periodic but not SHM