In a simple harmonic motion, let f be the acceleration and T be the time period. If x denotes the displacement, then |fT| vs. x graph will look like:
The Correct Option is B
Solution and Explanation
The |fT| vs. x graph for a simple harmonic motion will have the following shape:
Starting from the origin (0,0), the graph will have an upward-sloping section. As the displacement (x) increases, the magnitude of acceleration (∣f∣) also increases. This part of the graph represents the acceleration getting stronger as the object moves away from the equilibrium position.
Eventually, the graph reaches a peak point, after which it starts to curve downward. The magnitude of acceleration starts decreasing as the displacement increases further.
At the extreme displacement points (maximum amplitude), the magnitude of acceleration is zero, and the graph crosses the x-axis.
This graph represents the behavior of acceleration (∣f∣) with respect to displacement (x) in a simple harmonic motion.
The correct answer is option (B):
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Concepts Used:
Simple Harmonic Motion
Simple Harmonic Motion is one of the most simple forms of oscillatory motion that occurs frequently in nature. The quantity of force acting on a particle in SHM is exactly proportional to the displacement of the particle from the equilibrium location. It is given by F = -kx, where k is the force constant and the negative sign indicates that force resists growth in x.
This force is known as the restoring force, and it pulls the particle back to its equilibrium position as opposing displacement increases. N/m is the SI unit of Force.
Types of Simple Harmonic Motion
Linear Simple Harmonic Motion:
When a particle moves to and fro about a fixed point (called equilibrium position) along with a straight line then its motion is called linear Simple Harmonic Motion. For Example spring-mass system
Conditions:
The restoring force or acceleration acting on the particle should always be proportional to the displacement of the particle and directed towards the equilibrium position.
- – displacement of particle from equilibrium position.
- – Restoring force
- - acceleration
Angular Simple Harmonic Motion:
When a system oscillates angular long with respect to a fixed axis then its motion is called angular simple harmonic motion.
Conditions:
The restoring torque (or) Angular acceleration acting on the particle should always be proportional to the angular displacement of the particle and directed towards the equilibrium position.
Τ ∝ θ or α ∝ θ
Where,
- Τ – Torque
- α angular acceleration
- θ – angular displacement