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Question
A mass M attached to a spring oscillates with a period of 2 seconds. If the mass is increased by 2 Kg, the eriod increases by 1 second. Find the initial mass, assuming that Hooke's law is obeyed.
Solution
Mass (M) = ?
Time period of a oscillating mass m attached to a spring is given by:
Time period is given by , T = `2pi sqrt ("M"/"K")`
where, T is the period, m is the mass and k is the spring constant.
T1 = 2s ,
T2 = 2 + 1 = 3s ,
m2 = m1 + 2
T1 = `2pi sqrt ("M"/"K")` .......(i)
T2 = `2pi sqrt (("M" + 2)/"K")` ........(ii)
From (i) and (ii)
`2/3 = sqrt ("M"/("M" + 2))`
Squaring both the sides,
`4/9 = "M"/("M" + 2)`
⇒ 4( m + 2 ) = 9m
⇒ 4m + 8 = 9m
⇒ 5m = 8
∴ M = 1.6 Kg
The initial mass attached to the spring is 1.6 Kg.
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