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makvit [3.9K]
3 years ago
12

for the simple harmonic motion d = 9cos (pi//2t), what is the maximum displacement from the equilibrium position?

Mathematics
2 answers:
Tpy6a [65]3 years ago
6 0
Y = A cos (B(x - C) + D

A gives the amplitude, which is the maximum displacement, so it's 9.
vivado [14]3 years ago
3 0

Answer:

The maximum displacement from the equilibrium position is 9.

Step-by-step explanation:

The given simple harmonic motion is:

d=9cos(\frac{\pi}{2}t)

Differentiating above equation with respect to t, we get

d'=-9sin(\frac{\pi}{2}t)(\frac{\pi}{2})

⇒d'=-\frac{9{\pi}}{2}sin(\frac{\pi}{2}t)

Again differentiating the above equation with respect to t, we have

d''=-\frac{9({\pi})^{2}}{4}cos(\frac{\pi}{2}t)

Now, d'=0

⇒-\frac{9{\pi}}{2}sin(\frac{\pi}{2}t)=0

⇒sin(\frac{\pi}{2}t)=0

⇒\frac{\pi}{2}t=0

⇒t=0

Substituting the value of t=0 in d, we get

⇒d=9cos(\frac{\pi}{2}(0))

⇒d=9cos(0)

⇒d=9(1)

⇒d=9

Therefore, the maximum displacement from the equilibrium position is d= 9.

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