TS EAMCET · Physics · Oscillations
A block is in simple harmonic motion (S.H.M) on the end of the spring with position given by \(x=(5) \cos \left(\omega t+\frac{\pi}{4}\right)\) If the total mechanical energy used is 100 J to achieve maximum displacement, then the potential energy at time t = 0 is
- A 20 J
- B 80 J
- C 75 J
- D 50 J
Answer & Solution
Correct Answer
(D) 50 J
Step-by-step Solution
Detailed explanation
\(x(0) = 5 \cos\left(\frac{\pi}{4}\right) = 5 \frac{\sqrt{2}}{2}\) \(PE = E \left(\frac{x}{A}\right)^2\) \(PE = 100 \left(\frac{5 \frac{\sqrt{2}}{2}}{5}\right)^2\) \(PE = 100 \left(\frac{\sqrt{2}}{2}\right)^2 = 100 \left(\frac{2}{4}\right) = 50\) J
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