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Chapter 1: Q89P (page 1)

A mass m is attached to a spring of force constant 75 N/m and allowed to oscillate. Figure P14.89 shows a graph of its velocity component \({v_x}\) as a function of time t. Find (a) the period, (b) the frequency, and (c) the angular frequency of this motion. (d) What is the amplitude (in cm), and at what times does the mass reach this position? (e) Find the maximum acceleration magnitude of the mass and the times at which it occurs. (f) What is the value of m?

Short Answer

Expert verified

(a) 1.6 s

Step by step solution

01

Given Data

\(\begin{array}{l}k = 75\;{\rm{N/m}}\\T = 1.6\;{\rm{s}}\;{\rm{(from}}\;{\rm{figure)}}\\{{\rm{v}}_{\max }} = 20\;{\rm{cm/s}}\end{array}\)

02

Concept

The time period is determined by finding the one complete duration of oscillation.

03

Step 3(a): Find the period

From the figure, we can get a time period.

T = 1.6 s

Hence the period is 1.6 s

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