Question 117: Oscillations

Question

The ratio of maximum acceleration to maximum velocity in a simple harmonic motion is 10 s
−1
. At, t = 0 the displacement is 5 m. What is the maximum acceleration ? The initial phase is ${\pi  \over 4}$.

Accepted Answer

Mximum velocity, V
max
= a$\omega $
Maximum acceleration, A
max
= a$\omega $
2
Given that,
${{a{\omega ^2}} \over {a\omega }}$ = 10
$ \Rightarrow $$\,\,\,$  $\omega $ = 10 s
$-$1
Displacement, x = a sin ($\omega $t + ${\pi  \over 4}$)
at t = 0,  displacement x = 5
$	herefore\,\,\,$ 5 = a sin $\left( {{\pi  \over 4}} ight)$
$ \Rightarrow $$\,\,\,$ 5 = a $ 	imes $ ${1 \over {\sqrt 2 }}$
$ \Rightarrow $$\,\,\,$ a = 5${\sqrt 2 }$
$	herefore\,\,\,$ Maximum acceleration,
A
max
= a$\omega $
2
= 5 ${\sqrt 2 }$ $ 	imes $ (10)
2
= 500 ${\sqrt 2 }$ m/s
2

Answer

500 m/s
2

Answer

500 $\sqrt 2 m/$ s
2

Answer

750 m/s
2

Answer

750 $\sqrt 2 $m / s
2

Oscillations

The ratio of maximum acceleration to maximum velocity in a simple harmonic motion is 10 s −1 . At, t = 0 the displacement is 5 m. What is the maximum acceleration ? The initial phase is {\pi \over 4}.

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