SHM Help (1 Viewer)

[dishab]

The temperature at each instant of a day can be modelled by a SHM function oscillating between 9 degrees at 4:00 AM and 19 degrees at 4:00PM. Find, correct to the nearest minute, the times between 4:00 AM and 4:00 PM when the temperature is 14 degrees.
The correct answer is 10AM. I am completely lost with this.

 

[kcqn93]

it's pretty simple lol

14 degrees is the mid point between 9 and 19

so you make that x = 0

at 4am, x = -5 and t=0

at 4pm, x = 5 and t=12

x = 5 cos(pi - pi/12 t)

when x = 0 .......... t = 6

at x = 0, it is 14 degrees

therefore its at 14 degree at 10am


if that made any sense... i'm bad at explaining lol sorry

 

[Neal Caffrey]

simplar harmonigc motions lol

 

[dishab]

how did u get x = 5 cos(pi - pi/12 t)

 

[kcqn93]

amplitude = 5

x = a cos(nt + @)

x = -5 and t=0

-5 = 5 cos(@)
-1 = cos(@)
@ = pi

x = 5 and t=12

5 = 5cos(12n + pi)
1 = cos(12n + pi)
0 = 12n + pi
12n = - pi
n = -pi/12

therefore x = 5 cos(pi - pi/12 t)

 

[dishab]

Thnx kcqn93