Question 142: 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/s2

Answer

500 $$\sqrt 2 m/$$ s2

Answer

750 m/s2

Answer

750 $$\sqrt 2 $$m / s2

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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