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Chapter 15: Q. 33 (page 416)

The amplitude of an oscillator decreases to36.8%of its initial value in10.0sWhat is the value of the time constant?

Short Answer

Expert verified

Time constant has the value of蟿=5s.

Step by step solution

01

Introduction.

Oscillation is the repeated or recurrent oscillation of a statistic around a central value or between two or more states, usually in time.

A physiological motion is clearly perceived by the term vibration. Oscillation can be seen in a pendulum bob and flow of electrons.

02

Explanation

A decelerated oscillator's output diminishes continuously with increasing:

A=A0e鈭�t2蟿

The time constant T is used here. When you use AA0=0.368 and the logarithmic function, you get

蟿=鈭�t2ln鈦�(0.368)=5s

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Most popular questions from this chapter

Interestingly, there have been several studies using cadavers to determine the moments of inertia of human body parts, information that is important in biomechanics. In one study, the center of mass of a 5.0 kg lower leg was found to be 18 cm from the knee. When the leg was allowed to pivot at the knee and swing freely as a pendulum, the oscillation frequency was 1.6Hz . What was the moment of inertia of the lower leg about the knee joint?

An object in simple harmonic motion has amplitude 8.0cmand frequency0.50Hz. At t=0sit has its most negative position. Write the function x(t)that describes the object鈥檚 position.

A 100gmass on a 1.0-m-long string is pulled 8.0掳to one side and released. How long does it take for the pendulum to reach4.0掳 on the opposite side?

What is the difference between the driving frequency and the natural frequency of an oscillator?

A block attached to a spring with unknown spring constant oscillates with a period of 2.0s.What is the period if

a. The mass is doubled?

b. The mass is halved?

c. The amplitude is doubled?

d. The spring constant is doubled? Parts a to d are independent questions, each referring to the initial situation.
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