Undamped spring system, need help

[flipjack]

undamped spring system, need urgent help

hey guys, got my maths exam tomorrow and this question seems to be confusing me, i think they made a mistake, but I am not sure, if anyone could show me how to do this question or what answer they found it would be greatly appreciated

question:A mass-spring system consists of a unit mass (that is m = 1kg) and a spring with
stiffness constant k = 9. A forced oscillation of this system without damping is
given by x'' + 16x = sin(2t)

where x(t) is the position of the mass at the time t. If the initial position of the
mass is x(0) = 0 and the initial velocity of it is x'(0) = 2, find the position x(t) of
this initial value problem

Their solution:
x(t) = (11/24)sin(4t)+(1/12)cos(2t)

my answer was colossal compared to theirs

 

[Mute]

Their solution:
x(t) = (11/24)sin(4t)+(1/12)cos(2t)

I think you (or your book) have a typo there: that should be a sine instead of a cosine. The cosine wouldn't satisfy the initial conditions.

Anyways, I indeed get x(t) = (11/24)sin(4t)+(1/12)sin(2t). I'm not sure what techniques you know so solve these things but I solved it using the Laplace transform method.

You should tell us how you tried to solve it so people can see what you did and tell you where you went wrong (or, perhaps that your solution is correct but you need to use some trig identities to get it down to the simpler form). In any event, you can always try to check your solution by differentiating and seeing if it satifies the DE.

 

[flipjack]

thanks mute,
i just played around with a few identities and managed to simplify it to the same answer as you