AP EAMCET · PHYSICS · Oscillations

A particle executes simple harmonic motion between $x = - A$ and $x = + A$ . If it takes a time $T_{1}$ to $g_{0}$ from $x = 0$ to $x = A / 2$ and $T_{2}$ to go from $x = A / 2$ to $x = A$ . Then

A $T_{1} < T_{2}$
B $T_{1} > T_{2}$
C $T_{1} = T_{2}$
D $T_{1} = 2 T_{2}$

Verified Solution

Answer & Solution

Correct Answer

(A) $T_{1} < T_{2}$

Step-by-step Solution

Detailed explanation

Equation of SHM x=asinωt at x=0 ; to=0 at x=A2from equation A2=asin2πTt1⇒t1=T12 at x=A from equation A=asin2πTt1⇒t1=T4 so time from x=0 to x=A2 T1=t1-to=T12 and time from x=A2 to x=A T2=t2-t1=T4-T12=T6 so…

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 particle executes simple harmonic motion between x=-A and x=+A. If it takes a time T1 to g0 from x=0 to x=A/2 and T2 to go from x=A/2 to x=A. Then

Step-by-step Solution

A particle executes simple harmonic motion between $x = - A$ and $x = + A$ . If it takes a time $T_{1}$ to $g_{0}$ from $x = 0$ to $x = A / 2$ and $T_{2}$ to go from $x = A / 2$ to $x = A$ . Then