The functionx = (8.9 m) cos[(5πrad/s)t + π/3 rad]gives the simple harmonic motion of a body. At t = 9.7 s, what are the (a) displacement, (b) velocity, (c) acceleration, and (d) phase of the motion? Also, what are the (e) frequency and (f) period of the motion?

Question
Asked Nov 17, 2019
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The function
x = (8.9 m) cos[(5πrad/s)t + π/3 rad]
gives the simple harmonic motion of a body. At t = 9.7 s, what are the (a) displacement, (b) velocity, (c) acceleration, and (d) phase of the motion? Also, what are the (e) frequency and (f) period of the motion?

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Expert Answer

Step 1

Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and specify the other subparts you’d like answered.

Given,

х 3 8.9сos| 5at +
3
t 9.7 s
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х 3 8.9сos| 5at + 3 t 9.7 s

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Step 2

If we compare given wave equation with standard wave equation then,

Standard Equation,x= cos(t+¢)
Given Equation,x=8.9cos 5zt-
3
If we compare both equation then,
Angular Frequency,a 5x
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Standard Equation,x= cos(t+¢) Given Equation,x=8.9cos 5zt- 3 If we compare both equation then, Angular Frequency,a 5x

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Step 3

Part (a):

Displacement at t...

x 8.9cos5nt
3
t 9.7 sec
-5x
x 8.9cos (9.7+
x 89cos48.5
3
x8.9cos(48.83)
x-7.70
x7.70 m
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x 8.9cos5nt 3 t 9.7 sec -5x x 8.9cos (9.7+ x 89cos48.5 3 x8.9cos(48.83) x-7.70 x7.70 m

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