11 grade physics others> If a simple pendulum oscillates with an a...
If a simple pendulum oscillates with an amplitude of 50 mm and time period of 2 sec, then its maximum velocity is: A. 0.6 m/s
B. 0.16 m/s
C. 0.8 m/s
D. 0.32 m/s
1 AnswersGiven Data:
• Amplitude of oscillation: A=50A = 50 mm = 0.05 m
• Time period: T=2T = 2 sec
Formula for Maximum Velocity in Simple Harmonic Motion:
The maximum velocity (vmaxv_{\text{max}}) of a simple pendulum undergoing simple harmonic motion (SHM) is given by:
vmax=Aωv_{\text{max}} = A \omega
where:
• AA is the amplitude
• ω\omega is the angular frequency, given by:
ω=2πT\omega = \frac{2\pi}{T}
Step-by-Step Calculation:
1. Calculate Angular Frequency:
ω=2πT=2π2=π rad/sec\omega = \frac{2\pi}{T} = \frac{2\pi}{2} = \pi \text{ rad/sec}
2. Calculate Maximum Velocity:
vmax=Aω=(0.05)×(π)v_{\text{max}} = A \omega = (0.05) \times (\pi) vmax=0.05×3.1416v_{\text{max}} = 0.05 \times 3.1416 vmax≈0.157 m/sv_{\text{max}} \approx 0.157 \text{ m/s}
Conclusion:
The closest answer choice is (B) 0.16 m/s.
Final Answer: (B) 0.16 m/s.
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