Solving a Simple Pendulum Problem with SHM Model

In summary, the maximum speed is v = 2Lf and the maximum angular acceleration is α = 10.0°/s. The maximum restoring force is F = ½mv^2.
  • #1
pandaXpress
6
0

Homework Statement



A simple pendulum has a mass of 0.250 kg and a length of 6.00 m. It is displaced through an angle of 10.0° and then released. Solve this problem by using the simple harmonic motion model for the motion of the pendulum.
(a) What is the maximum speed?


(b) What is the maximum angular acceleration?


(c) What is the maximum restoring force?



Homework Equations


1[tex]\stackrel{}{}2[/tex]mv[tex]^{}2[/tex] = mgh
this is kinetic energy = potential energy.

The Attempt at a Solution


I tried using the above equation to find maximum speed, but I found that I was getting the wrong answer because I used arc length in the height variable instead of the actual height.
So I guess I'm asking.. how to find height?
Do I use some Pythagorean?
Or just some algebra/trig.. -.-

and also.. what it means "maximum resisting force"?
 
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  • #2


oops.. the equation is 1/2mv^2 = mgh..
i accidentally did it wrong.. sorry!
 
  • #3
Welcome to PF!

Hi pandaXpress ! Welcome to PF! :smile:
pandaXpress said:
Solve this problem by using the simple harmonic motion model for the motion of the pendulum.

Do what the question says … start with a standard shm equation.
and also.. what it means "maximum resisting force"?

erm :redface: … it's restoring force … and they just mean "force" :wink:
 
  • #4


Hmm.. which shm equation would that be?
My teacher gave us many for different types of waves..
would this be considered a "double open" wave?

so, I would use
v = 2Lf?
and then, where would I use mass or angle?


thanks tiny-tim~~!
 
  • #5
pandaXpress said:
Hmm.. which shm equation would that be?
My teacher gave us many for different types of waves..
would this be considered a "double open" wave?

oooh … no idea what your're talking about …

i thought there was only one shm equation? :redface:
so, I would use
v = 2Lf?
and then, where would I use mass or angle?

shm has force proportional to (minus) distance …

so what's the force in terms of the distance? :wink:
 
  • #6


ooh, wait is it the equation for velocity on a string?

v = sqrt(FL/m)
so, in this case I guess F (tension) would have to be mass times gravitational force?
and then I could find velocity, right?
 
  • #7


Or.. (I just found this on the Internet..)

x(t) = Acos(2 X pi X f X t + phase of oscillation (pi/2, pi/4, etc)

is this that standard one you were talking about?
 
  • #9


ooh, kay.
I can see from there.

hey, thank you very much~!
 

What is a simple pendulum?

A simple pendulum is a weight suspended from a string or rod that is able to swing back and forth freely. It is a common physics tool used to study the behavior of oscillating systems.

How does the SHM model apply to a simple pendulum?

The SHM (simple harmonic motion) model is used to describe the motion of a simple pendulum. This model assumes that the pendulum follows a sinusoidal pattern of motion with a constant amplitude and period.

What factors affect the period of a simple pendulum?

The period of a simple pendulum is affected by the length of the string or rod, the mass of the weight, and the acceleration due to gravity. Other factors such as air resistance and friction can also have a small impact.

How do you solve a simple pendulum problem using the SHM model?

To solve a simple pendulum problem using the SHM model, you will need to know the length and mass of the pendulum, as well as the acceleration due to gravity. Then, you can use the formula T = 2π√(L/g) to calculate the period of the pendulum.

What are some real-life applications of simple pendulums?

Simple pendulums have numerous real-life applications, including timekeeping devices such as grandfather clocks and metronomes. They are also used in seismometers to measure earthquakes and in engineering to test the stability of structures. Additionally, simple pendulums are used in physics education to demonstrate concepts of oscillations and SHM.

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