Simple pendulum problem with only velocity and angle known

[mmoadi]

Homework Statement

We push a weight hanging on a long string in a horizontal direction so that the velocity at the beginning is v = 10 cm / s. What is the oscillating time of such a pendulum, if the string on which hangs deviates the most for θ = 5 º?

Homework Equations

T = 2pie[sqrt(L/g)]

The Attempt at a Solution

Calculating the length of the string:

v² = 2gL[1-cosθ] → L= v² / 2g[1-cosθ]
L= 0.3 cm

Calculating the oscillating time:

T = 2pie[sqrt(L/g)]
T= 0.35 s

Are my calculations correct?
Thank you for helping!

 

[John Park]

You're told that the weight hangs on a "long" string, and it is given a speed of 10 cm/sec. Does it seem reasonable that L = 0.35 cm = 3.5 mm ?

From your equation for v², what is v when θ = 0? Does that seem reasonable if the pendulum is oscillating?

What is the energy of the pendulum (assume a mass m for the weight on the end of the string)? How is it distributed between kinetic energy and potential energy? What condition determines the extent of the swing?

 

[gneill]

John, don't wait for a response from the OP; The last time the OP was logged in was back in 2010 and is thus unlikely to see your probing questions.

This problem is in the Open Practice Problems forum and as such you are free to go ahead and provide a complete solution.