For the next three questions, consider a system oscillating according to the functionx (t) = A cos(@t + p)%3Dwhereandofare unknown constants, andA = 4.5 cm%DThe following initial conditions(t = 0)are given:x (0) = 2.5 cma (0) = –8.0 cm/s?v (0) > 0V. 4.What is the oscillator's maximum speed?cannot determine from information given0.83 cm/s7.7 cm/s3.7 cm/s2.5 cm/s

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Description: For the next three questions, consider a system oscillating according to the functionx (t) = A cos(@t + p)%3Dwhereandofare unknown constants, andA = 4.5 cm%DThe following initial conditions(t = 0)are given:x (0) = 2.5 cma (0) = –8.0 cm/s?v (0) > 0V.

Answered: What is the oscillator's maximum speed?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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4.
What is the oscillator's maximum speed?
cannot determine from information given
0.83 cm/s
7.7 cm/s
3.7 cm/s
2.5 cm/s

Expert Solution

Step 1

Given

$x (0) = 2.5 cm a (0) = - 8.0 cm / s^{2}$

The acceleration of the oscillator is

$a (0) = - ω^{2} x (0) ω is the angular velocity of the oscillator .$

The angular velocity is

$ω = \sqrt{\frac{a (0)}{x (0)}} = \sqrt{\frac{8.0 cm / s^{2}}{2.5 cm}} = 1.8 rad / s$

Step 2

The amplitude of oscillation A=4.5 cm

The maximum velocity of the oscillator is

$v_{\max} = Aω v_{\max} = (4.5 cm) (1.8 rad / s) v_{\max} = 8.1 cm$

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