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Chapter 23: Problem 2781
Complete the following sentence. Time period of oscillation of a simple pendulum is dependent on......... (A) Length of thread (B) initial phase (C) amplitude (D) mass of bob
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In the experiment of simple pendulum, we have taken a thread of $140 \mathrm{~cm}\(, and an amplitude of \)5 \mathrm{~cm}$ to begin with. Here \(\theta\) to begin with is about........ (A) \(5^{\circ}\) (B) \(8^{\circ}\) (C) \(2^{\circ}\) (D) \(3^{\circ}\)
In the experiment of simple pendulum we keep \(\theta<5^{\circ}\), so as ensure \(\ldots \ldots \ldots\) (A) mass \(\mathrm{m}\) does not interfere in the time period (B) \(\mathrm{g}\) remains constant (C) the air drag is not too much (D) \(\sin \theta \cong \theta\) where by motion becomes simple harmonic.
What is the equation for a damped oscillator, where \(\mathrm{k}\) and \(\mathrm{b}\) are constants and \(\mathrm{x}\) is displacement. (A) $\left\\{\left(\mathrm{md}^{2} \mathrm{x}\right) /\left(\mathrm{dt}^{2}\right)\right\\}+\mathrm{kx}+\\{(\mathrm{dbx}) /(\mathrm{dt})\\}=0$ (B) $\left\\{\left(\mathrm{md}^{2} \mathrm{x}\right) /\left(\mathrm{dt}^{2}\right)\right\\} \times \mathrm{kx}=\\{(\mathrm{dbx}) /(\mathrm{d} \mathrm{t})\\}$ (C) $m\left\\{\left(d^{2} x\right) /\left(d t^{2}\right)\right\\}=k x+\\{(d b x) /(d t)\\}$ (D) $\left\\{\left(\mathrm{md}^{2} \mathrm{x}\right) /\left(\mathrm{dt}^{2}\right)\right\\}-\mathrm{kx}=\mathrm{b}\\{(\mathrm{d} \mathrm{x}) /(\mathrm{dt})\\}$
Complete the following sentence. In a damped oscillation of a pendulum......... (A) the sum of potential energy and kinetic energy is conserved. (B) mechanical energy is not conserved (C) the kinetic energy is conserved (D) the potential energy is conserved
In a damped oscillation with damping constant \(b\). The time taken for its mechanical energy to drop to half. What is its value? (A) \((\mathrm{b} / \mathrm{m}) \ln 2\) (B) \((\mathrm{b} / 2 \mathrm{~m}) \ln 2\) (C) \((\mathrm{m} / \mathrm{b}) \ln 2\) (D) \((2 \mathrm{~m} / \mathrm{b}) \ln 2\)
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