Simple Harmonic Motion; help needed! (1 Viewer)

[NizDiz]

Hey guys, this is a really easy question however I aint getting it right, may someone please help me. A body in SHM has an amplitude of 10m and period of 10 s. How long would it take for body to travel from one of its extremities of its path of motion to a point 4 metres away? I got 1.85s, but answers say 1.5s. Why?? Thanks

 

[HeroicPandas]

Starts from 1 extremity, a = 10, T = 10, n = pi/5

Assume centre of motion is 0

Lets pick 1 extremity, left or right? i'll pick right (begins at x = 10)

x = acos(nt) (For right extreme) OR x = -acos(nt) (For Left extreme)

Since right extreme we pick x = acos(nt)

x = 10cos(pi t/5)

"one of its extremities of its path of motion to a point 4 metres away"

From 1 extremity (we picked x = 10) to a point 4 metres away from the extremity (where am I know in 4 units if i started at x = 10?), so to the point x = 6

let x = 6,

6 = 10cos(pi t/5)

...
...
t = 1.478 + k(10) (where k is an integer)

let k =0, t = 1.5 (rounded up 1dp)

 

[NizDiz]

Ur a legend! thanks champion!! But why pick 10, can it be any number or is it 10, since i amplitude, then 10-4=6, therefore x=6?

 

[HeroicPandas]

Ur a legend! thanks champion!! But why pick 10, can it be any number or is it 10, since i amplitude, then 10-4=6, therefore x=6?

I made the centre of motion x = 0 (origin), and since amplitutde is 10, the 2 extremities are x = -10 and x = 10

U can make the centre of motion be x= 1 if u like, so extremities are x = -9 and x = 11 (since amplitutde is 10)


In response to ur bolded part - yes
From 1 extremity (we picked x = 10) to a point 4 metres away from the extremity (where am I know in 4 units if i started at x = 10?), so to the point x = 6

 

[NizDiz]

ok cool, thanks a lot