posted by Robert C .
Suppose that a simple pendulum consists of a small 66.0 g bob at the end of a cord of negligible mass. Suppose that the angle between the cord and the vertical is given by
θ = (0.0800 rad) cos[(4.30 rad/s)t + ϕ]
(a) What is the pendulum's length?
(b) What is its maximum kinetic energy?
I figured out a) by using w=2pi/T
T=1.46 then used T to solved T=(2pi*sq root L/g) L = .53 but I can't figure out an equation to give me the velocity. Any ideas?
(a) w = 4.40 rad/s
is the angular frequency, sqrt(g/L)
Solve for L, the pendulum length
L = g/w^2
(b) Max velocity Vmax = = L*theta*w
Maximum KE = (1/2) M Vmax^2
You are right about L = 0.53. Don't forget the units (meters)
In simple harmonic motion,
max velocity = w*(Amplitude) and
max acceleration = w^2*(Ampitude)
In your case I had to add an L factor to get linear velocities from the angular amplitude.
Where did the Vmax = L*theta*w
come from? How do I find theta?
Theta should be theta-max, the angular amplitude, which is 0.0800 radians
Sorry about that
Vmax= (.53m)(.0800rad)(4.30 rad/s)
=.0011 or 1.09e-03
That doesn't look right to me. what am I doing wrong? ;_;
Another question, sorry, trying my bests to understand your thinking. I don't see where you knew to multiple L * theta * W.
I understand that the 2nd derivative of the equation gives you the Velocity function.
No, the first derivative of your theta vs t (multiplied by L) gives you the velocity function.
L*theta_max is the displacement amplitude (in small angle approximation) ; so
is the maximum velocity