Simple Harmonic Motion Questions (1 Viewer)

[Shadowulf]

these questions are just bugging me at the moment, i missed a few lessons on simple harmonic motion so im not sure what im meant to get for these

1.
Show that these are simple harmonic motion:
x = 10 + 8sin2t + 5cos2t
x = sqrt3cos2t - sin2t

2. A ship needs 10m of water to pass down a channel safely. At low tide, the channel is 9m deep and at high tide, 12m deep. Low tide is at 10am and high tide at 5pm. Assume that the tidal motion is simple harmonic
a) State the amplitude and period of the motion
b) At what time can the ship safely proceed before midnight?

for 2, i want to know how to work out a) >.<

 

[nickthebiscuit]

For the first two qs show that the 2nd derivative = -w^2 x

ie. differentiate twice n then manipulate to get into that form

as for the 2nd q, cbb =P somebody else can do it =]

 

[b0b444]

its been a while since i've done these but this is what i think for 2.

it says to assume that the motion of the tide is simple harmonic. in other words, a graph of the height of the tide versus time would look like a sine wave. now for part a.) you just have to remember the definitions. what is amplitude? and what is period? amplitude is the distance from the centre of the simple harmonic motion to a maximum or minimum. So here you are given the minimum and maximum of the motion (low and high tide) so the centre of the motion has to be in the middle of the given interval. this makes it 10.5 . so from this point to say the maximum, 12, is 1.5m. this is the amplitude.

the period is the time taken for the sine wave to execute 1 wavelength of motion. so here it is 1 day because that is the time it takes to go from 1 high tide to the next (or low tide for that matter).

 

[Shadowulf]

Thanks guys got it all now ty ^^