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 2.89 s to travel from x= 0.090 m to x= -0.090 m .

Part A

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.

t = sec

Part B

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.

t = sec

Explanation / Answer

a) amplitude A = 0.090 m

time periode T = 2.89*2 = 5.78 sec

from x = 0.18 to -0.18 m

T = 2pisqrt(m/k)

T = 5.78/2 = 2.89 sec

b) w = 2pi/T = 2*3.14/5.78 = 1.086 rad/s

from the relation

x = Asin(wt)

0.09 = 0.18sin(1.086*t)

t = 0.482 s

total time taken t = 2*0.482 = 0.964 sec

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