A small block is attached to an ideal spring and is moving in SHM on a horizonta

Question

A small block is attached to an ideal spring and is moving in SHM on a horizontal, frictionless surface. When the amplitude of the motion is 0.090 m, it takes the block 2.51 s to travel from x = 0.090 m to x = -0.090 m. If the amplitude is doubled, to 0.180 m, how long does it take the block to travel from x = 0.180 m to x = --0.180 m? Express your answer to two significant figures and include the appropriate units. If the amplitude is doubled, to 0.180 m, how long does it take the block to travel from x = 0.090 m to x = -0.090 m? Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

(a) how long does it take the block to go from x= 0.18m to x= - 0.18 m
The period remains the same and hence the time to travel the two extremes remains the same as 2.51 s

(b) From x= 0.09 m to x= -0.09 m the time taken is 3.15 – 0.45 = 2.7 s (half the period)

x =0.18 sin (2t/5.02)
When (2t1/5.02) =/6, sin /6 = 0.5 and x = 0.09 m
When (2t2/5.02) = (/6 + ), sin (/6 + ) = -0.5 and x = -0.09 m
Solving
t1 = 0.42 s and t2 =2.93 s

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