IIT JEE , AIEEE Forum - Physics , Mechanics

shakirshafi12

condition for SHM
a=-w^2.x
displacement=Asin(wt+Q)
any expression expressible in this form is an SHM

part (i)
sin t-cos t
sqroot(2)(sin tcos45-cos tsin45)
sqroot(2)sin(t-45)
hence (i) is shm
part(ii)
sin^3 t
sin3t=3sint-4sin^3t
sin^3t=(3sint-sin3t)/4--------1
multiply and divide eq by 3/sqroot(10)
and we will not be able to express equation in the form
y=asin(wt+Q)
hence (ii)
is also an not S.H.M but it will be periodic
for eq (iii)
3 cos ( 1/(4-2 t)) if it is that way
this function is non periodic and not an S.H.M
(iv)cos t+cos3 t+cos5 t
cos 5t+cos3t+cost
=2cos4t*cost+cost
=cost(2cos 4t+1)
it is inexpressible in the form
y=asin(wt+Q)
hence it is not an S.H.M
but it is a periodic function

(v)e- 2t2 vi 1+ t+ 2t2 simply cannot be periodic

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