Simple harmonic oscillators and a pendulum clock.

In summary, simple harmonic oscillators are systems that follow a predictable pattern of motion, oscillating back and forth between two points due to a restoring force. These types of oscillators can be found in various objects, such as pendulums, which are commonly used in clocks to keep time. The motion of a pendulum is governed by the laws of physics, specifically the relationship between its length and the gravitational force acting on it. By understanding the principles of simple harmonic motion, we can better understand and appreciate the workings of a pendulum clock.
  • #1
clayton26
4
0
Hey physics forums, this is my first post and frankly I'm having trouble conceptualizing this problem. I know harmonic oscillation is involved, as it is a pendulum. However, I know I have to incorporate g into the s.h.o. equation and I'm not quite sure how to do that. Any help would be greatly appreciated.


Homework Statement


A pendulum clock which keeps correct time at a point where g=9.8 m/s^2 is found to lose 10 seconds per day at a higher altitude where the gravitational field now has a new value g(n). What is the numerical value of this g(n)?


Homework Equations


This is from the force diagrams I've drawn.
Tcos(theta)-mg=ma(x)
Tsin(theta)=ma(y)

I'm lost. Please help!
 
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  • #2
clayton26 said:
Hey physics forums, this is my first post and frankly I'm having trouble conceptualizing this problem. I know harmonic oscillation is involved, as it is a pendulum. However, I know I have to incorporate g into the s.h.o. equation and I'm not quite sure how to do that. Any help would be greatly appreciated.


Homework Statement


A pendulum clock which keeps correct time at a point where g=9.8 m/s^2 is found to lose 10 seconds per day at a higher altitude where the gravitational field now has a new value g(n). What is the numerical value of this g(n)?


Homework Equations


This is from the force diagrams I've drawn.
Tcos(theta)-mg=ma(x)
Tsin(theta)=ma(y)

I'm lost. Please help!

The period of a pendulum with small amplitude - like you find on a clock - is related to the length [which doesn't change] and g [which is changing]
I think this problem is more about proportional or percentage change than re-deriving the formula for a pendulum.
The other trick is to work out whether the clock is running fast or slow in the mountains, and what that says about the pendulum.
 
  • #3
Are you expected to derive the period of a pendulum from first principles, or can you use the (well known) formula directly? It can be found in a few seconds with a web search.
 

1. What is a simple harmonic oscillator?

A simple harmonic oscillator is a system in which a particle or object oscillates back and forth around an equilibrium position due to a restoring force that is proportional to its displacement from the equilibrium point. This type of motion is characterized by a constant period and amplitude.

2. How does a pendulum clock work?

A pendulum clock is a type of simple harmonic oscillator that uses a pendulum to keep time. The clock's mechanism includes a weight or spring that provides energy to the pendulum, causing it to swing back and forth. As the pendulum oscillates, it triggers the clock's escapement mechanism, which keeps track of the time by counting the number of oscillations.

3. What factors affect the period of a simple harmonic oscillator?

The period of a simple harmonic oscillator is affected by three main factors: the mass of the object, the stiffness of the restoring force, and the amplitude of the oscillation. The period is directly proportional to the mass and the stiffness, and inversely proportional to the amplitude. In other words, increasing the mass or stiffness will increase the period, while increasing the amplitude will decrease the period.

4. Can the period of a pendulum clock be affected by external factors?

Yes, the period of a pendulum clock can be affected by external factors such as changes in temperature, air resistance, and the length of the pendulum. These factors can cause the period to either increase or decrease, resulting in the clock running too fast or too slow. To maintain accuracy, pendulum clocks often have a mechanism to adjust the length of the pendulum.

5. What are some real-world applications of simple harmonic oscillators?

Simple harmonic oscillators have many practical applications, including in musical instruments, such as guitar strings and piano wires. They are also used in mechanical systems, such as shock absorbers and springs in cars. In addition, simple harmonic oscillators are essential components in technologies such as pendulum clocks, seismographs, and electronic circuits.

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