Question

The focus of particle based on the time is given by x=A cos(bt), y=A sin(bt).what is the nature of the force acting on the particle

Answer 1

Answer:

Simple harmonic with amplitude

A

2

+B

2

The motion of particle is S.H.M with

x=Asinωt+Bcosωt=asin(ωt+θ)

Where a=

A

2

+B

2

, A=acosθ, B=asinθ, θ=tan

−1

B/A

Answer 2

Answer:

The nature of the force acting on the particle is a central force directed towards the origin, with a magnitude proportional to the distance from the origin.

Explanation:

The force acting on a particle with position given by x = A cos(bt) & y = A sin(bt),  we can calculate its acceleration using the second law of motion, which states that the force acting on an object is equal to its mass times its acceleration.

Taking the time derivativs of the given eqtns:, we can find the velocity and acceleration of the particle as follows:

v = dx/dt = -A b sin(bt) i + A b cos(bt) j

a = dv/dt = -A b^2 cos(bt) i - A b^2 sin(bt) j

The nature of the force acting on the particle is determined by its accl. , which is ⇔ to the -ve of the position vctr.

The force acting on the particle is always directed towards the origin, with a magnitude proportional to the distance from the origin.

The force acting on the particle depends only on the distance from the origin and is directed towards the origin

This is a characteristic feature of the inverse square law of force, which is found in many physical systems, such as gravitational and electrostatic interactions

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