Question

A spring hanging from the ceiling vibrates up and down. Its vertical position at time t is given by f (t)  4sin3t. Find the velocity position at time t . What is the spring’s maximum speed? What is its location when it reaches its maximum speed.

Answer 1

first derivative is 12cos(3t).which is velocity.
and the maximum speed is 12 coz maximum value of cos is 1and if u put 1 in equation f't=12cos(3t) in place of cos(3t) u get maximum speed which is 12.now when u have maximum speed 12 and u know t=0 because cos(3t)=1 only when 3t=0 as cos0=1.so now put t=0 in first equation f(t)=4sin(3t) and you get location which is zero.