TS EAMCET · Physics · Mechanical Properties of Solids

A simple harmonic oscillator of frequency $1 Hz$ has a phase of $1$ radian. By how much should the origin be shifted in time so as to make the phase of the oscillator vanish. (time in seconds).

A $- \frac{1}{π} s$
B $- \frac{1}{2 π} s$
C $- \frac{π}{2} s$
D $- π s$

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Answer & Solution

Correct Answer

(B) $- \frac{1}{2 π} s$

Step-by-step Solution

Detailed explanation

Given: Frequency of the simple harmonic oscillator f=1 Hz , and phase θ=1 radian The expression of the phase of a simple harmonic oscillator is stated as θ=ωt, where ω is the angular velocity, t is the time. ω=θt, Since…

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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A simple harmonic oscillator of frequency 1 Hz has a phase of 1 radian. By how much should the origin be shifted in time so as to make the phase of the oscillator vanish. (time in seconds).

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A simple harmonic oscillator of frequency $1 Hz$ has a phase of $1$ radian. By how much should the origin be shifted in time so as to make the phase of the oscillator vanish. (time in seconds).