A horizontal platform with an object placed on it is executing SHM .the amplitude of oscillation is 0.1m what must be the least period of these oscillation so that the object is not detached from the platform?

Question

Answer

Detachment of Object in SHM

- The maximum acceleration experienced by an object in simple harmonic motion (SHM) is at the extreme points of its oscillation, which is when the object is at the amplitude.
- The maximum acceleration can be calculated using the formula a_max = ω^2 * A, where ω is the angular frequency and A is the amplitude.
- In order to prevent the object from detaching from the platform, the maximum acceleration should not exceed the gravitational acceleration, which is approximately 9.81 m/s^2.

Calculating the Least Period

- The period of oscillation in SHM can be calculated using the formula T = 2π / ω, where T is the period and ω is the angular frequency.
- To find the least period required so that the object is not detached from the platform, we need to ensure that the maximum acceleration is less than the gravitational acceleration.
- Substituting the values into the formula a_max = ω^2 * A, we get ω = √(a_max / A).
- Substituting this value of ω into the formula T = 2π / ω, we can calculate the least period required for the object to remain on the platform.

By following these calculations, you can determine the least period of oscillation required for the object to not detach from the platform during SHM.

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