pretty stuck on this one, any help apreciated:
the angular displacement (feta) of a shaft is given by feta= 1/2 (cos-5t. Find the velcoity of the shaft w at t= 2s
my apologies for the improper layout.
Post what you have so far (:
Im afraid i don't even know where to get started. im new to my course and i havent studyied anything like this before.
No problem! I can help you with that.
To find the velocity of the shaft at t = 2s, we need to differentiate the angular displacement equation with respect to time.
Given: θ = (1/2) cos(-5t)
Taking the derivative of θ with respect to time t will give us the velocity w(t):
w(t) = dθ/dt
To differentiate the equation, we can apply the chain rule. The derivative of cos(u) is -sin(u), and the derivative of -5t with respect to t is -5.
Therefore, applying the chain rule, we have:
w(t) = dθ/dt = (1/2) * (-5) * sin(-5t)
Now, we substitute t = 2s into the equation to find the velocity at t = 2s:
w(2) = (1/2) * (-5) * sin(-5*2)
Simplifying the expression within the sine function:
w(2) = (1/2) * (-5) * sin(-10)
Now, we evaluate the sine function:
w(2) = (1/2) * (-5) * sin(-10)
= (1/2) * (-5) * (-0.1736)
= 0.433
Therefore, the velocity of the shaft at t = 2s is 0.433 units/s.
Please note that the units were not specified in the given equation, so the answer is in arbitrary units.