TS EAMCET · Physics · Mechanical Properties of Solids

The displacement of a particle in simple harmonic motion (SHM) is given by $y = \sqrt{3 π} \sin (\frac{100}{π} t + \frac{π}{4}) .$ What will be the displacement of the particle from the mean position when its kinetic energy is eight times that of its potential energy?

A $\sqrt{\frac{π}{3}}$
B $\sqrt{\frac{3 π}{2}}$
C $\sqrt{π}$
D $\sqrt{3 π}$

Verified Solution

Answer & Solution

Correct Answer

(A) $\sqrt{\frac{π}{3}}$

Step-by-step Solution

Detailed explanation

The formula of kinetic energy and potential energy in S.H.M. K.E.=12mω2A2-y2 & P.E.=12mω2y2 , in the question given that, K.E.=8P.E.⇒12mω2A2-y2=8×12mω2y2⇒A2-y2=8y2⇒9y2=A2⇒y=±A3 Now in the above equation,…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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The displacement of a particle in simple harmonic motion (SHM) is given by y=3πsin100πt+π4. What will be the displacement of the particle from the mean position when its kinetic energy is eight times that of its potential energy?

Step-by-step Solution

The displacement of a particle in simple harmonic motion (SHM) is given by $y = \sqrt{3 π} \sin (\frac{100}{π} t + \frac{π}{4}) .$ What will be the displacement of the particle from the mean position when its kinetic energy is eight times that of its potential energy?