Question

A small block is attached to an ideal spring and moving in SHM on a horizontal frictionless table. When the amplitude of the motion is 0.090m, it takes the block 2.70s to travel from x=0.090m to -0.090m. If the amplitude is doubled to 0.180m, how long does it take to travel a) from x=0.180m to x=-0.180m, and b) from x=0.09m to -0.09m?

Answer 1

http://upload.wikimedia.org/wikipedia/en/math/f/e/e/fee6809cefc85d3f7924bf6a7d0a8d94.png

Answer 2

seems that time period does not change

Answer 3

right, The period would be 5.4 seconds right?

Answer 4

yeah

Answer 5

ok, so we can find the angular frequency with that

Answer 6

angular frequency also does not change as Time period does not change

Answer 7

ok, so we need to use the equation x=Acos(wt+phi) right?

Answer 8

i think so ... for the second part

Answer 9

sorry I just don't know how to proceed

Answer 10

do you know what is the answer of a?

Answer 11

no I don't

Answer 12

i will take the same amount of time

Answer 13

2.7 s? howcome?

Answer 14

you know what is SHM??

Answer 15

yup simple harmonic motion

Answer 16

where the restoring force is linear in the displacement from the equilibrium position.

Answer 17

so wait, T is always the same? because k is the same?

Answer 18

yes ... T depends on
\[\sqrt{m/k}\]
which is not changed

Answer 19

ok cool thanks, so now what for b?

Answer 20

let's see, we have formula
y = A sin(wt+phi) right

and we know the position of y, and we know angular frequency, amplitude, and if we suppose phase angle to zero ... we have phi=0

Answer 21

why do we suppose phase angle is zero?

Answer 22

because it doesn't matter, since we are taking the difference of two variables, initial conditions don't matter.

Answer 23

A=0.18, y=-0.090, w=1.1636?

Answer 24

w = 2pi/T