Finding times when mass passes downward at 3 ft/s on spring

[CR9]

Hey guys,

So I was trying to do a few questions to prepare for my Differential Equations exam soon, and I stumbled upon this question:

A mass of 1 slug is suspended from a spring whose spring constant is 9lb/ft. The mass is initially released from a point 1 foot above the equilibrium position with an upward velocity of square root 3 ft/s. Find the times at which the mass is heading downward at a velocity of 3 ft/s.

What I did was I took downward as positive while downward as negative. But I only managed to get 1 value for t, which is 0.6s.

My equation for the motion was x(t)= -cos 3t - (square root 3/ 3) sin 3t

Please help me...Thanks !

 

[Mark44]

Hey guys,

So I was trying to do a few questions to prepare for my Differential Equations exam soon, and I stumbled upon this question:

A mass of 1 slug is suspended from a spring whose spring constant is 9lb/ft. The mass is initially released from a point 1 foot above the equilibrium position with an upward velocity of square root 3 ft/s. Find the times at which the mass is heading downward at a velocity of 3 ft/s.

What I did was I took downward as positive while downward as negative. But I only managed to get 1 value for t, which is 0.6s.

My equation for the motion was x(t)= -cos 3t - (square root 3/ 3) sin 3t

Please help me...Thanks !

You're showing us your solution to an initial value differential equation, but you haven't shown us the differential equation you started with. Show us the complete initial value problem and your work - it's possible you made an error somewhere.