S.h.m Homework Help: Find Length, Velocity & Acceleration

[Mattmiles]

Homework Statement

A simple pendulum is observed to perform 40 oscillations, of amplitude 40 in 100 seconds. Find:
i) the length of the pendulum
ii) the maximum angular velocity of the pendulum bob
iii) the maximum angular acceleration of the bob

The Attempt at a Solution

i) L=g/4pi^2xT^2 = 1.55meters
ii) ?
iii) ?

 

[Disconnected]

Homework Statement

A simple pendulum is observed to perform 40 oscillations, of amplitude 40 in 100 seconds. Find:
i) the length of the pendulum
ii) the maximum angular velocity of the pendulum bob
iii) the maximum angular acceleration of the bob

The Attempt at a Solution

i) L=g/4pi^2xT^2 = 1.55meters
ii) ?
iii) ?

Think about at what point in the bob's motion it will have the greatest speed. It may help to draw a graph. Perhaps it is when the bob is passing through the equilibrium position, just before the restoring force starts to decelerate it?
In that case it is at it's lowest point, so all of the potential energy it possesses at it's maximum displacement (try drawing some triangles) will be in the form of kinetic energy at the equilibrium point.

The method for finding the acceleration is similar. Remember that the force exerted by the restoring force is proportional to the displacement from the equilibrium position, and that f=ma. So at what point would the force, and therefore the acceleration, be the highest? Concentrate at that point.

 

[Mattmiles]

The bobs Max Velocity will be when it is mid-way between it's maximum displacement. This is also it's point of minimum velocity. But I am still stumped. Sorry.

 

[Disconnected]

The bobs Max Velocity will be when it is mid-way between it's maximum displacement. This is also it's point of minimum velocity. But I am still stumped. Sorry.

Okay. If you have a pendulem length of 1.55m, an amplitude of 40(units?) you can use trig to find what thedistance between the bob and the will be at maximum displacement. Draw a wee picture.

[PLAIN]http://img694.imageshack.us/img694/6267/shmx.jpg

You can see that there is a change of height, yes? So the difference in gravitational potential energy at the top of the swing (maximum displacement) and the bottom of the swing (maximum velocity) will be equal to the kinetic energy at the equilibrium position, right?Edit to add: X in the diagram is the difference in height.
Second edit: This assumes that the amplitude refers to sideways motion, not arclength.

 

[HallsofIvy]

The bobs Max Velocity will be when it is mid-way between it's maximum displacement. This is also it's point of minimum velocity. But I am still stumped. Sorry.

Well, it can't be both can it? By "conservation of energy" the bob will have maximum speed at its lowest point, minimum at its highest.