Formula Sheet for Simple Harmonic Motion (Part 1)

Introduction:
Simple Harmonic Motion (SHM) is a type of periodic motion where an object oscillates back and forth around its equilibrium position with a constant amplitude and frequency.

Equations:
The following equations are used to describe the motion of an object undergoing SHM:

1. Displacement (x) from equilibrium position:
x = A cos(ωt + φ)

2. Velocity (v) of the object:
v = -Aω sin(ωt + φ)

3. Acceleration (a) of the object:
a = -Aω^2 cos(ωt + φ)

Variables:
The variables used in the SHM equations are:

1. Amplitude (A): The maximum displacement of the object from its equilibrium position.

2. Angular frequency (ω): The rate at which the object oscillates, measured in radians per second.

3. Phase constant (φ): The initial angle of the object at t = 0.

Other Formulas:
The following formulas are also useful in SHM:

1. Period (T): The time taken for one complete oscillation.
T = 2π/ω

2. Frequency (f): The number of oscillations per unit time.
f = 1/T

3. Maximum velocity (vmax): The maximum velocity of the object during its motion.
vmax = Aω

4. Maximum acceleration (amax): The maximum acceleration of the object during its motion.
amax = Aω^2

Conclusion:
These equations and formulas are essential for understanding and solving problems related to SHM. By using these equations, we can calculate various parameters of the motion, such as displacement, velocity, acceleration, period, frequency, maximum velocity, and maximum acceleration.