And object is undergoing simple harmonic motion along the x-axis. Its position is described as a function of time by x(t) = 1.6 cos(3.5t – 1.4), where x is in meters, the time, t, is in seconds, and the argument of the cosine is in radians. a)Find the amplitude of the simple harmonic motion, in meters.b)What is the value of the angular frequency, in radians per second?c)Determine the position of the object, in meters, at the time t = 0.d)What is the object’s velocity, in meters per second, at time t = 0?e)Calculate the object’s acceleration, in meters per second squared, at time t = 0.f)What is the magnitude of the object’s maximum acceleration, in meters per second squared?

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Asked Nov 20, 2019
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And object is undergoing simple harmonic motion along the x-axis. Its position is described as a function of time by x(t) = 1.6 cos(3.5t – 1.4), where x is in meters, the time, t, is in seconds, and the argument of the cosine is in radians. 

a)Find the amplitude of the simple harmonic motion, in meters.

b)What is the value of the angular frequency, in radians per second?

c)Determine the position of the object, in meters, at the time t = 0.

d)What is the object’s velocity, in meters per second, at time t = 0?

e)Calculate the object’s acceleration, in meters per second squared, at time t = 0.

f)What is the magnitude of the object’s maximum acceleration, in meters per second squared?

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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,

Position of wave, x(t)1.6cos(3.5t-1.4)
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Position of wave, x(t)1.6cos(3.5t-1.4)

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Step 2

Standard equation of wave is given by below,

x 4cos(-
A Amplitude of wave in m
x Position of object in m
Angular Frequency in (rad/sec)
Phase Difference in radian
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x 4cos(- A Amplitude of wave in m x Position of object in m Angular Frequency in (rad/sec) Phase Difference in radian

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Step 3

Part (a):

Amplitude of simple ...

x()1.6cos(3.5t-1.4)
If we compare given equation with standard equation,
Then,Amplitude(A)=1.6 m
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x()1.6cos(3.5t-1.4) If we compare given equation with standard equation, Then,Amplitude(A)=1.6 m

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