Mathmatical model of a pendulum

In summary: Instead, use the given information to find the value of k, and then use that value in the general equation A(t) = A e^-kt to find an equation expressing the amplitude A in terms of time t.In summary, the problem involves finding an equation for the amplitude A of a pendulum with a decreasing amplitude over time. Using the given information, the value of k can be determined and substituted into the general equation A(t) = A e^-kt to find the desired equation in terms of time t.
  • #1
bju
1
0

Homework Statement


Suppose the pendulum string is attached to a point on the ceiling 30 cm from the wall. The weight is moved away from its rest position and released at time t=0. At time t=1.4 sec, it reaches its maximum distance from the wall, 37.4 cm away, and then swings back toward the wall again. At times 2.8 sec, the weight reaches a minimum distance of 23.2 cm form the wall, and then swings away again.
Assuming that the amplitude of the pendulum's swing decreases exponentially with time, find an eqaution expressing the amplitude A in terms of time t.

Homework Equations


A(t)=A e^-kt

The Attempt at a Solution


I tried A(t)= A e^-kt , A= (37.4-23.2)/2=7.1 Don't know what to do next?
 
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  • #2
bju said:

Homework Statement


Suppose the pendulum string is attached to a point on the ceiling 30 cm from the wall. The weight is moved away from its rest position and released at time t=0. At time t=1.4 sec, it reaches its maximum distance from the wall, 37.4 cm away, and then swings back toward the wall again. At times 2.8 sec, the weight reaches a minimum distance of 23.2 cm form the wall, and then swings away again.
Assuming that the amplitude of the pendulum's swing decreases exponentially with time, find an eqaution expressing the amplitude A in terms of time t.

Homework Equations


A(t)=A e^-kt

The Attempt at a Solution


I tried A(t)= A e^-kt , A= (37.4-23.2)/2=7.1 Don't know what to do next?

Your function does not allow the pendulum bob to oscillate (i.e., swing back and forth).
 

Related to Mathmatical model of a pendulum

1. What is a mathematical model of a pendulum?

A mathematical model of a pendulum is a simplified representation of a real-world pendulum using mathematical equations and principles. It allows us to understand and analyze the behavior of a pendulum without having to physically observe or experiment with it.

2. How is a mathematical model of a pendulum created?

A mathematical model of a pendulum is created by using mathematical equations that describe the motion of the pendulum. These equations take into account factors such as the length of the pendulum, the mass of the pendulum, and the force of gravity.

3. What information can be obtained from a mathematical model of a pendulum?

A mathematical model of a pendulum can provide information about the motion of the pendulum, such as its amplitude, period, and frequency. It can also help us understand how changing certain variables, such as the length of the pendulum, can affect its motion.

4. How accurate is a mathematical model of a pendulum?

The accuracy of a mathematical model of a pendulum depends on the complexity of the model and the variables that are taken into account. Generally, a simple model will have some degree of error, but as the model becomes more complex and includes more variables, it can become more accurate.

5. What are the practical applications of a mathematical model of a pendulum?

A mathematical model of a pendulum has practical applications in fields such as physics, engineering, and astronomy. It can help us understand the behavior of pendulums in different situations and can be used to design and optimize pendulum-based devices, such as clocks and seismometers.

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