Simple Harmonic Motion Pendulum problem

In summary, the conversation discusses finding the maximum speed of a simple pendulum released from rest at an angle of 10 degrees to the vertical. The solution involves calculating the amplitude of oscillation using the equation A=0.3-0.3cos10, and then finding the maximum velocity at the lowest point of the pendulum's swing. However, there is a discrepancy in the solution and further discussion is needed to determine the correct answer.
  • #1
bobbricks
32
0

Homework Statement


A simple pendulum of length =30.0cm is released from rest from an angle of θ=10.0∘ to the vertical.
Assuming that the pendulum undergoes simple harmonic motion, find its maximum speed.

Source: https://isaacphysics.org/questions/accuracy_shm_pendulum_num

Homework Equations


a) v=wA
b) T=2pi*root(L/g) --possibly?

The Attempt at a Solution


A=0.3-0.3cos10
w=2pi/T
so w=root(g/L) by subbing equation a) into b).
g=9.81 and L=0.3.

so v=root(9.81/0.3)*(0.3-0.3cos10)
=0.02606... ms^(-1)

But that isn't the correct answer?
 
Physics news on Phys.org
  • #2
A is the amplitude of oscillation, not the length of the pendulum.
 
  • #3
Is A=0.3-0.3cos10 ?
 
  • #4
Bump
 
  • #5
bobbricks said:
Is A=0.3-0.3cos10 ?

How did you come up with this number? How far away from the equilibrium is the pendulum when it is at an angle of 10 degrees?
 
  • #6
Its maximum velocity will be at the lowest point. The total length is 0.3m. Its current vertical height distance from the top is 0.3cos10. So the difference is 0.3-0.3cos10 which is the maximum amplitude..?
 

Related to Simple Harmonic Motion Pendulum problem

1. What is Simple Harmonic Motion (SHM)?

Simple Harmonic Motion is a type of periodic motion where an object moves back and forth along a straight line, with its acceleration proportional and in the opposite direction of its displacement from a fixed point.

2. How does a pendulum demonstrate SHM?

A pendulum consists of a mass attached to a fixed point by a string or rod. When the mass is displaced from its equilibrium position and then released, it will swing back and forth in a regular pattern due to the force of gravity. This motion demonstrates SHM as the acceleration of the mass is always directed towards the equilibrium point.

3. What factors affect the period of a pendulum's oscillation?

The period of a pendulum's oscillation, or the time it takes for one complete swing, is affected by three main factors: the length of the pendulum, the mass of the pendulum, and the strength of the gravitational field. The longer the pendulum, the longer the period. The greater the mass of the pendulum, the longer the period. And the stronger the gravitational field, the shorter the period.

4. How can the equation T = 2π√(l/g) be used to solve SHM pendulum problems?

This equation, known as the pendulum period formula, can be used to calculate the period of a pendulum based on its length (l) and the strength of the gravitational field (g). It can also be rearranged to solve for other variables, such as the length or gravitational field, in a given SHM pendulum problem.

5. Are there any real-life applications of SHM pendulum problems?

Yes, there are many real-life applications of SHM pendulum problems. For example, pendulums are used in clocks to keep time, in seismographs to measure earthquakes, and in amusement park rides to create thrilling swinging motions. The principles of SHM are also applied in engineering and physics to study vibrations and waves.

Similar threads

  • Introductory Physics Homework Help
Replies
1
Views
879
  • Introductory Physics Homework Help
Replies
1
Views
857
  • Introductory Physics Homework Help
Replies
16
Views
421
  • Introductory Physics Homework Help
2
Replies
51
Views
2K
  • Introductory Physics Homework Help
Replies
5
Views
934
  • Introductory Physics Homework Help
Replies
7
Views
974
  • Introductory Physics Homework Help
Replies
14
Views
507
  • Introductory Physics Homework Help
Replies
17
Views
972
  • Introductory Physics Homework Help
Replies
9
Views
727
  • Introductory Physics Homework Help
Replies
1
Views
1K
Back
Top