THE PROBLEM 0.37 m/s2. The top of a skyscraper sways back and forth in simple ha

Question

THE PROBLEM 0.37 m/s2. The top of a skyscraper sways back and forth in simple harmonic motion with maximum speed0.062 m/s and maximum acceleration (a) Calculate the angular frequency. (b) Calculate the period. (c) Calculate the amplitude PAPER SOLUTION Solve the problem on paper first, including all four IDEA steps. You will become a better physicist that way! Have you finished your paper solution already? yes o no INTERPRET DEVELOP (a) Derive an algebraic expression for the angular frequency. (b) Derive an algebraic expression for the period (c) Derive an algebraic expression for the amplitude

Explanation / Answer

We are given,

vmax = 0.062 m/s, amax = 0.37 m/s^2

Use eqns,

vmax = A --------------(1)

amax = A2 -------------(2)

a)

Divide (2) by (1),

A2/A = amax/vmax

= amax/vmax

Plugging values,

= 0.37/0.062

= 5.97 rad/s

b)

T=2/ = = (2*3.14)/(5.97)

T = 1.05 s

c)

From (1),

A= vmax/

Plugging values,

A= 0.062/5.97

A= 0.01m

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