Finding the angle of a pendulum in SHM

In summary, the clock pendulum starts oscillating at a frequency of 1.5 Hz and an initial angle of 20° to the vertical. At t=0.25s, the angle of the pendulum is 20*cos(2π*0.25/0.67) degrees.
  • #1
t246335
2
0

Homework Statement


A clock pendulum oscillates at a frequency of 1.5 Hz. At t = 0, it is released from rest starting at an angle of 20° to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at the following times? (Hint: Do not confuse the angle of swing θ of the pendulum with the angle that appears as the argument of the cosine.)
Find the angle at t = 0.25 s



Homework Equations



T=1/f x=Acos(2pit/T) feta=2pi(t/T)

The Attempt at a Solution


T=1/1.5 T=.67sec feta=2pi(.25sec/.67)
 
Physics news on Phys.org
  • #2
Pay attention to that hint! In this question, the amplitude is 20 degrees and equation of motion gives the angle at other times:
θ = 20*cos(2πt/T)
 

Related to Finding the angle of a pendulum in SHM

1. What is SHM?

SHM stands for Simple Harmonic Motion. It is a type of periodic motion in which a system moves back and forth around a stable equilibrium point. Examples of SHM include a pendulum swinging back and forth or a mass on a spring oscillating up and down.

2. How is the angle of a pendulum in SHM measured?

The angle of a pendulum in SHM can be measured by using a protractor or by using a motion sensor and graphing software to track the angle over time. The angle is typically measured from the vertical line of the pendulum's equilibrium point.

3. What factors affect the angle of a pendulum in SHM?

The angle of a pendulum in SHM is affected by the length of the pendulum, the mass of the pendulum bob, and the strength of the gravitational field. It is also affected by any external forces acting on the pendulum, such as air resistance or friction.

4. How is the angle of a pendulum related to its period?

The angle of a pendulum is directly related to its period, or the time it takes for one complete back and forth motion. As the angle increases, the period also increases. This relationship is known as Hooke's law and can be described by the equation T=2π√(l/g), where T is the period, l is the length of the pendulum, and g is the acceleration due to gravity.

5. Can the angle of a pendulum in SHM be used to determine the strength of the gravitational field?

Yes, the angle of a pendulum in SHM can be used to determine the strength of the gravitational field. By measuring the period and length of the pendulum, the acceleration due to gravity (g) can be calculated using the equation g=4π²l/T². This is known as the pendulum's period of oscillation method for measuring gravity.

Similar threads

For a Pendulum: Knowing Acceleration Find Maximum Angle
    • Introductory Physics Homework Help
Replies
26
Views
2K
Foucault Pendulum at the North Pole
    • Introductory Physics Homework Help
Replies
9
Views
771
How to find the maximum angle of a pendulum after a mass collides with it
    • Introductory Physics Homework Help
Replies
4
Views
3K
Find the position of a pendulum as a function of time?
    • Introductory Physics Homework Help
Replies
1
Views
2K
Calculating Amplitude in Simple Harmonic Motion
    • Introductory Physics Homework Help
Replies
1
Views
2K
What Happens to a Pendulum's Period at 90 Degrees Inclination?
    • Introductory Physics Homework Help
Replies
13
Views
3K
Differential equation for a pendulum
    • Introductory Physics Homework Help
Replies
5
Views
1K
Finding g from a Compound Pendulum Graph
    • Introductory Physics Homework Help
Replies
3
Views
7K
How Do I determine when a pendulum ceases to be SHM
    • Introductory Physics Homework Help
Replies
2
Views
2K
Angular velocity of a simple pendulum
    • Introductory Physics Homework Help
Replies
2
Views
5K

Hot Threads

Recent Insights

Back
Top