SHM/Pendulum Prob: Solving Last 2 Parts of the Problem

  • Thread starter Koncept
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In summary, the conversation discusses a pendulum with specific dimensions and mass that is oscillating about its equilibrium position. The questions pertain to calculating the angular velocity, frequency, amplitude, maximum angle, and kinetic energy of the pendulum at different positions. The attempted solutions include values for the first four questions, but further assistance is needed for the last two questions regarding the speed and location of the kinetic energy on the pendulum's cycle.
  • #1
Koncept
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0

Homework Statement


I'm stuck on the last 2 parts of this problem and would really appreciate any help!

A pendulum of length 2m and mass 1kg oscillates about its equilibrium position. At time 1s it has a displacement of 20cm. Assume that (phi symbol) = 0 rad.


Homework Equations



a) Its angular velocity

b) the frequency of oscilation

c) the amplitude

d) the maximum angle from the verticle made by the pendulum

e) the speed of the pendulum is given by v(t) = w(ang. vel)A(amplitude)cos(wt+phi). Calculate the kinetic energy at positions theta = 0 rad and theta = 1/2 pi rad

f) where on the pendulum's cycle do these energies occur and why are they different?

The Attempt at a Solution


 
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  • #2

You need to show some sort of attempt. If it moves with SHM, what is the general form of its motion? x(t) = ?
 
  • #3
These are the answers I got:

A) 2.21 ms^-1

B) 0.35Hz

C) 0.25m

D) 0.13 rads

E) ?

F) ?
 

Related to SHM/Pendulum Prob: Solving Last 2 Parts of the Problem

1. What is SHM (Simple Harmonic Motion)?

SHM is a type of periodic motion in which a body or object oscillates back and forth around a central point with a constant amplitude and period. It is often described as a wave-like motion and can be seen in various systems such as pendulums, springs, and rotating objects.

2. How does a pendulum work?

A pendulum works by converting potential energy into kinetic energy and back again. When the pendulum is at its highest point, it has maximum potential energy due to its height. As it swings down, this potential energy is converted into kinetic energy, and at the bottom of the swing, all of the energy is kinetic. As the pendulum swings back up, this kinetic energy is converted back into potential energy. This back and forth motion continues as long as there is no external force acting on the pendulum.

3. How is the period of a pendulum determined?

The period of a pendulum is determined by its length and the acceleration due to gravity. The longer the pendulum, the longer its period, and the shorter the pendulum, the shorter its period. The period is also affected by the amplitude of the swing, but this effect is negligible for small swings. The acceleration due to gravity is a constant value of 9.8 m/s^2 on Earth, which means that the period of a pendulum is the same regardless of its mass.

4. How do you solve the last two parts of a SHM/pendulum problem?

The last two parts of a SHM/pendulum problem typically involve finding the velocity and acceleration of the pendulum at a specific point in its motion. To solve these parts, you can use the equations for SHM, which relate the position, velocity, and acceleration of the pendulum. These equations can be derived from the laws of motion and energy conservation principles.

5. What factors can affect the motion of a pendulum?

The motion of a pendulum can be affected by several factors, such as the length of the pendulum, the amplitude of the swing, and the mass of the pendulum. Other external factors, such as air resistance and friction, can also affect the motion of a pendulum. Additionally, the acceleration due to gravity can vary slightly depending on the location on Earth and the altitude.

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