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A mass suspended from a spring oscillates in simple harmonic motion at a frequency of 4 cycles per second. The distance from the highest to
Question
A mass suspended from a spring oscillates in simple harmonic motion at a frequency of 4 cycles per second. The distance from the highest to the lowest point of the oscillation is 100 cm. Find an equation that describes the distance of the mass from its rest position as a function of time. Assume that the mass is at its lowest point when t = 0.
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Physics
4 years
2021-07-27T18:00:26+00:00
2021-07-27T18:00:26+00:00 2 Answers
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Answers ( )
Answer:
Explanation:
Given that,
Frequency of oscillation is
f = 4cycle per second
The distance from the highest to the lowest point of the oscillation is 100 cm
this is the distance from the minimum amplitude to the maximum amplitude i.e. 2A
Amplitude of oscillation
2A = 100cm = 1m
A = 1/2
A = 0.5m
An object position in simple harmonic motion (SHM) Is modelled generally as
y = A•Sin(wt)
Or
y = A•Cos(wt)
Since the amplitude is minimum at t=0
Then, the best modelled for this is
y = A•Cos(wt)
We know that, A= 0.5m
We know that,
w = 2πf
Then, w = 2π × 4
w = 8πrad/s
Then, the position of the mass at any time becomes
y = A•Cos(wt)
y = 0.5 • Cos(8πt)
Answer:
Explanation:
The general equation for a simple harmonic motion is
when we take the beginning of the motion in an extreme an the oscillation. If the motion starts in the lowest point we have
where A is the amplitude, w is the angular frequency, t is the time and x is the position.
In this case the amplitude is 50cm, because a complete oscillation is about 100cm.
For w we have
Hence, the equation is
HOPE THIS HELPS!!