a particle moving with simple harmonic motion performs 10 complete oscillations per minute and its speed when a distance of 80mm from the centre of oscillationsis 3/5 of maximum speedfind the amplitude of oscillations
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a particle moving with simple harmonic motion performs 10 complete oscillations per minute and its speed when a distance of 80mm from the centre of oscillationsis 3/5 of maximum speedfind the amplitude of oscillations
answer is in picture
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Answer
Using the relation
v=
w
2
A 2
v is the velocity as displacement x, A :Amplitude]
From given
(i) when
x=
8,v=
3
3=
w
A 2
(1)
(ii) when
x=
6,v=
4
4=
w
A 2
(2)
dividing
(1)÷
(2)
gives
(
4
3
) 2
=
A 2 − 3 6
A 2 − 6 4
⇒
A 2
7
16×64−9×36
= 100
⇒ A= 10 cm
Putting A in (1) gives
3=
w
10
2
−64
⇒
w=
6
3
=
2
1
rad/s
∴ Time period ocsillaion
T=
w
2π
= 4π
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