# 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

(a) What is the pendulum's length?

(b) What is its maximum kinetic energy?

1. 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?

2. (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

3. 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.

4. Where did the Vmax = L*theta*w
come from? How do I find theta?

5. Theta should be theta-max, the angular amplitude, which is 0.0800 radians

=.182

KE=1/2mv^2
=1/2(.066kg)(.182)^2
=.0011 or 1.09e-03
That doesn't look right to me. what am I doing wrong? ;_;

7. 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.

8. 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
w*L*theta_max
is the maximum velocity