A small block is attached to an ideal spring and is moving in SHM on a horizonta
ID: 1485983 • Letter: A
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