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Question

A 150 g block oscillates in SHM on the end of a spring with k=1500 N/m, according to the relation x=x0cos(ωt+ϕ). How long does the block take to move from the position +0.800 x0 to +0.600 x0 directly ?

A
2 ms
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B
0.3 ms
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C
4 ms
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D
3 ms
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Solution

The correct option is D 3 ms
Given that
mass of block (m)=150 g or 0.15 kg
spring constant (k)=1500 N/m.
Equation of SHM, x=x0cos(ωt+ϕ)
We know that,
ω=km
From the given data,
ω=15000.15=100 rad/s

Equation of SHM is x=x0cos(ωt+ϕ)
Let t1 be the time at which x=+0.8x0.
Then, 0.8x0=x0cos(ωt+ϕ)
ωt1+ϕ=cos1(0.8)=0.6435 rad .....(1)

Similarly, when it at x=+0.6x0 at time t2,
ωt2+ϕ=cos1(0.6)=0.9272 rad ....(2)

From (1) and (2),
|ω(t2t1)|=0.2837 rad
t2t1=0.2837ω=0.28371003 ms

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