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Chapter 15: Q7CQ (page 472)

The mechanical energy of an undamped block–spring system is constant as kinetic energy transforms to elastic potential energy and vice versa. For comparison, explain what happens to the energy of a damped oscillator in terms of the mechanical, potential, and kinetic energies.

Short Answer

Expert verified

When a damped oscillator is decreasing gradually and permanently, the mechanical energy of a damped oscillator is changing back and forth between the potential and kinetic energy and is transforming to internal energy.

Step by step solution

01

The Mechanical Energy

The addition of the potential energy and the kinetic energy is the total amount of mechanical energy.

02

Step 2: Explain what happens to the energy of a damped oscillator

When a damped oscillator is decreasing gradually and permanently, the mechanical energy of a damped oscillator is changing back and forth between the potential and kinetic energy and is transforming to internal energy.

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Most popular questions from this chapter

A $65.0 - kg$ bungee jumper steps off a bridge with a light bungee cord tied to her body and to the bridge. The unstretched length of the cord isrole="math" localid="1660198723821" $11.0 m$ . The jumper reaches the bottom of her motion role="math" localid="1660198746464" $36.0 m$ below the bridge before bouncing back. We wish to find the time interval between her leaving the bridge and her arriving at the bottom of her motion. Her overall motion can be separated into an role="math" localid="1660198763301" $11.0 - m$ free fall and a role="math" localid="1660198776457" $25.0 - m$ section of simple harmonic oscillation. (a) For the free-fall part, what is the appropriate analysis model to describe her motion? (b) For what time interval is she in free fall? (c) For the simple harmonic oscillation part of the plunge, is the system of the bungee jumper, the spring, and the Earth isolated or non- isolated? (d) From your response in part (c) find the spring constant of the bungee cord. (e) What is the location of the equilibrium point where the spring force balances the gravitational force exerted on the jumper? (f) What is the angular frequency of the oscillation? (g) What time interval is required for the cord to stretch by role="math" localid="1660198795390" $25.0 m$ ? (h) What is the total time interval for the entirerole="math" localid="1660198809416" $36.0 - m$ drop?

A simple pendulum can be modeled as exhibiting simple harmonic motion when $θ$ is small. Is the motion periodic when $θ$ is large?

A small object is attached to the end of a string to form a simple pendulum. The period of its harmonic motion is measured for small angular displacements and three lengths. For lengths of $1.000 m$ , $0.750 m$ , and $0.500 m$ , total time intervals for 50 oscillations of $99.8 s$ , $86.6 s$ and $71.1 s$ are measured with a stopwatch. (a) Determine the period of motion for each length. (b) Determine the mean value of $g$ obtained from these three independent measurements and compare it with the accepted value. (c) Plot $T^{2}$ versus $L$ and obtain a value for $g$ from the slope of your best-fit straight-line graph. (d) Compare the value found in part (c) with that obtained in part (b)

The position of an object moving with simple harmonic motion is given by $x = 4 \cos (6 π t)$ , where x is in meters and t is in seconds. What is the period of the oscillating system? (a) $4 s$ (b) $\frac{1}{6} s$ (c) $\frac{1}{3} s$ (d) $6 π s$ (e) impossible to determine from the information given.

A simple pendulum is suspended from the ceiling of a stationary elevator, and the period is determined. (i) When the elevator accelerates upward, is the period (a) greater, (b) smaller, or (c) unchanged? (ii) When the elevator has a downward acceleration, is the period (a) greater, (b) smaller, or (c) unchanged? (iii) When the elevator moves with constant upward velocity, is the period of the pendulum (a) greater, (b) smaller, or (c) unchanged?

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