1. Reference Book is

2. LINEAR MOMENTUM AND ITS CONSERVATION
The linear momentum P of a particle of mass m moving with a velocity v is defined to be the product of the mass and velocity:
Linear momentum is a vector quantity because it equals the product of a scalar quantity m and a vector quantity v. Its direction is along v, it has dimensions ML/T, and its SI unit is kg m/s.

3. * Using Newton’s second law of motion, we can conclude that “ The time rate of change of the linear momentum of a particle is equal to the net force acting on the particle”

4. Conservation of Momentum for
a Two-Particle System
Applying Newton’s second law to each particle, we can write
Newton’s third law tells us that F12 and F21 are equal in magnitude and opposite in direction. That is, they form an action–reaction pair F12 , F21. We can express this condition as

5. Conservation of momentum
Because the time derivative of the total momentum ptot p1 p2 is zero, we conclude that the total momentum of the system must remain constant:
where pli and p2i are the initial values and p1f and p2f the final values of the momentum during the time interval dt over which the reaction pair interacts.
Conservation of momentum
Whenever two or more particles in an isolated system interact, the total momentum of the system remains constant.

6. SIMPLE HARMONIC MOTION
An object moves with simple harmonic motion whenever its acceleration is proportional to its displacement from some equilibrium position and is oppositely directed.
Applying Newton’s second law to the motion of the block, together with equation relates a force that is proportional to the displacement which is given by Hooke’s law , so :

7. The units of f are cycles per second s-1, or hertz (Hz).
In general, a particle moving along the x axis exhibits simple harmonic motion when x, the particle’s displacement from equilibrium, varies in time according to the relationship
The period T of the motion : is the time it takes for the particle to go through one full cycle.
The frequency: represents the number of
oscillations that the particle makes per unit time
The units of f are cycles per second s-1, or hertz (Hz).

8. THE PENDULUM
When is small, a simple pendulum oscillates in simple harmonic motion about the equilibrium position θ. The restoring force is mg sin θ , the component of the gravitational force tangent to the arc.

9. Where θ max is the maximum angular displacement
if we assume that θ is small, we can use the approximation sin θ = θ ; thus the equation of motion for the simple pendulum becomes
Where θ max is the maximum angular displacement
and the angular frequency is
Therefore, can be written as

10. The period of the motion is
The period and frequency of a simple pendulum depend only on the length of the string and the acceleration due to gravity.
The simple pendulum can be used as a timekeeper because its period depends only on its length and the local value of g. It is also a convenient device for making precise measurements of the free-fall acceleration.

11. The Foucault pendulum at the Franklin Institute in Philadelphia
The Foucault pendulum at the Franklin Institute in Philadelphia. This type of pendulum was first used by the French physicist Jean Foucault to verify the Earth’s rotation experimentally. As the pendulum swings, the vertical plane in which it oscillates appears to rotate as the bob successively knocks over the indicators arranged in a circle on the floor.
In reality, the plane of oscillation is fixed in space, and the Earth rotating beneath the swinging pendulum moves the indicators into position to be knocked down, one after the other.