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Contact [7]
4 years ago
7

A mass hanging from a vertical spring is in simple harmonic motion as given by the following position function, where t is measu

red in seconds and s is in inches: s(t)=−3cos(πt+π4). Determine the position of the spring at t=1.5 s. Find the velocity of the spring at t=1.5 s.
Physics
1 answer:
amid [387]4 years ago
6 0

Answer:

The position and velocity of the spring is −2.12 inches and -6.66 ft/s.

Explanation:

Given that,

The position function,

s(t)=-3\cos(\pi t+\dfrac{\pi}{4})

We need to calculate the position of the spring at t = 1.5 s

Using position function

s(t)=-3\cos(\pi t+\dfrac{\pi}{4})

Put the value of t in the function

s(1.5)=-3\cos(\pi\times1.5+\dfrac{\pi}{4})

s(1.5)=-2.12\ inches

We need to calculate the velocity of the spring

Using position function

s(t)=-3\cos(\pi t+\dfrac{\pi}{4})

On differentiating

\dfrac{ds}{dt}=3\pi\sin(\pi t+\dfrac{\pi}{4})

v(t)=3\pi\sin(\pi t+\dfrac{\pi}{4})

Put the value into the formula

v(1.5)=3\pi\sin(1.5\pi+\dfrac{\pi}{4})

v(1.5)=-6.66\ ft/sec

Hence, The position and velocity of the spring is −2.12 inches and -6.66 ft/s.

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