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Chapter 23: Problem 2782

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

Short Answer

Expert verified
In a damped oscillation of a pendulum, mechanical energy is not conserved (Option B). This is because energy is continually being lost from the system due to various factors, such as air resistance and friction.

Step by step solution

01

Define Damped Oscillation

Damped oscillation refers to an oscillating system where energy dissipation is present. In the case of a pendulum, this energy loss typically occurs due to air resistance and friction within the pendulum's pivot point. Over time, the amplitude of oscillation decreases, and the motion eventually stops.
02

Energy Conservation

Energy conservation states that, in a closed system with no external forces, the total mechanical energy (sum of potential and kinetic energy) remains constant throughout the system's motion. However, in a damped oscillation like the pendulum situation, energy is gradually lost, which means the total mechanical energy is not conserved.
03

Option A: Sum of potential and kinetic energy is conserved

As discussed above, in a damped oscillation, energy is continually being lost from the system due to various factors (e.g., friction and air resistance). Therefore, the sum of potential and kinetic energy is not conserved, and this option is incorrect.
04

Option B: Mechanical energy is not conserved

In a damped oscillation, mechanical energy is continuously being lost (due to factors such as air resistance and friction). This means that this option is correct: in a damped oscillation of a pendulum, mechanical energy is not conserved.
05

Option C: Kinetic energy is conserved

Since energy loss is happening in a damped oscillation due to factors like air resistance and friction, the pendulum's kinetic energy isn't conserved. Therefore, this option is incorrect.
06

Option D: Potential energy is conserved

In a damped oscillation of a pendulum, the pendulum loses height and, consequently, loses potential energy due to factors such as friction and air resistance. As a result, potential energy is not conserved, which means this option is also incorrect. Based on the analysis above, the correct answer is: (B) Mechanical energy is not conserved.

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Most popular questions from this chapter

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

If the time period of undamped oscillation is \(\mathrm{T}\) and that of damped oscillation is \(\mathrm{T}^{\prime}\), then what is the relation between \(\mathrm{T} \& \mathrm{~T}^{\prime}\) (A) \(\mathrm{T}^{\prime}<\mathrm{T}\) (B) nothing can be said, unless the drag force constant is known. (C) \(\mathrm{T}^{\prime}=\mathrm{T}\) (D) \(\mathrm{T}^{\prime}>\mathrm{T}\)

In a damped oscillation with damping constant \(b\). The time taken for amplitude of oscillation to drop to half what is its initial value? (A) \((\mathrm{b} / \mathrm{m}) \ln 2\) (B) (b / \(2 \mathrm{~m}) \ln 2\) (C) \((\mathrm{m} / \mathrm{b}) \ln 2\) (D) \((2 \mathrm{~m} / \mathrm{b}) \ln 2\)

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) \((2 \mathrm{~m} / \mathrm{b}) \ln 2\)

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) $\left\\{\left(\mathrm{md}^{2} \mathrm{x}\right) /\left(\mathrm{dt}^{2}\right)\right\\}-\mathrm{kx}=\mathrm{b}\\{(\mathrm{d} \mathrm{x}) /(\mathrm{dt})\\}$
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