Simple pendulum problem with only velocity and angle known

Click For Summary
SUMMARY

The discussion centers on calculating the oscillation time of a simple pendulum with a known initial velocity of 10 cm/s and a maximum angle of deviation of 5 degrees. The derived length of the string is 0.3 cm, leading to an oscillation period of 0.35 seconds using the formula T = 2π√(L/g). Participants question the reasonableness of the calculated string length and the energy distribution between kinetic and potential energy during the pendulum's motion.

PREREQUISITES
  • Understanding of simple harmonic motion principles
  • Familiarity with pendulum equations, specifically T = 2π√(L/g)
  • Knowledge of energy conservation in mechanical systems
  • Basic trigonometry, particularly in relation to angles and cosine functions
NEXT STEPS
  • Explore the derivation of the pendulum period formula T = 2π√(L/g)
  • Investigate the effects of varying angles on pendulum motion
  • Learn about energy conservation in pendulum systems, focusing on kinetic and potential energy distribution
  • Examine the impact of initial velocity on the amplitude and period of oscillation
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and oscillatory motion, as well as educators seeking to understand pendulum dynamics and energy conservation principles.

mmoadi
Messages
149
Reaction score
0

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!
 
Last edited:
Physics news on Phys.org
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?
 
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.
 

Similar threads

JEE solution wrong? (tempco of a clock)
  • · Replies 14 ·
Replies
14
Views
2K
Foucault Pendulum at the North Pole
  • · Replies 9 ·
Replies
9
Views
3K
For a Pendulum: Knowing Acceleration Find Maximum Angle
  • · Replies 26 ·
Replies
26
Views
4K
Seeking advice on "simple" pendulum problem
  • · Replies 27 ·
Replies
27
Views
2K
Simulating a Rotary Inverted Pendulum in Python
  • · Replies 15 ·
Replies
15
Views
2K
How to parametrize motion of a pendulum in terms of Cartesian coordinates?
  • · Replies 1 ·
Replies
1
Views
1K
Angular velocity of a simple pendulum
  • · Replies 2 ·
Replies
2
Views
6K
Work done on a conical pendulum
  • · Replies 3 ·
Replies
3
Views
3K
Angle that makes kinetic and potential energy of simple pendulum equal
  • · Replies 2 ·
Replies
2
Views
2K
Differential Equation for a Pendulum
  • · Replies 21 ·
Replies
21
Views
3K