Simple Harmonic motion problems

In summary, Simple Harmonic Motion (SHM) is a type of periodic motion characterized by a sinusoidal pattern of motion. It is affected by factors such as the mass of the object, spring constant, and amplitude of oscillations, which determine its period and frequency. The period of SHM can be calculated using the formula T = 2π√(m/k), and it can be thought of as a projection of circular motion onto a straight line. SHM has various real-life applications, including in pendulum clocks, musical instruments, and shock absorbers, as well as in modeling systems with periodic motion.
  • #1
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http://sweb.uky.edu/~lsadam0/problem2.JPG


Im kinda lost on this problem. Shouldnt the Y motion be described as A*sin(wt)?

In there equation we are considering when x=0, so the kx term is removed, but where is this third term coming from, and then should Y motion just be described as Asin(-wt-o)?
 
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  • #2
Nope,unless,at t=0 the amplitude is zero.Nope,the III-rd term is called "initial phase" and should not be missing when writing the general solution.

Daniel.
 
  • #3


Thank you for sharing this problem. Simple harmonic motion problems can be tricky, but with some practice and understanding of the concepts, they can be easily solved.

First, let's break down the given equation for x(t):

x(t) = A*cos(wt + ϕ) + C

We can see that the amplitude (A) and the angular frequency (w) are given. The phase angle (ϕ) and the constant (C) are yet to be determined.

Now, looking at the problem, we are given the initial conditions: x(0) = 0 and v(0) = 0.

Plugging in t=0 in the given equation, we get:

x(0) = A*cos(0 + ϕ) + C

Since x(0) = 0, we can conclude that C = 0.

Next, we need to determine the phase angle (ϕ).

Using the given initial velocity (v(0) = 0), we can find ϕ by differentiating x(t) with respect to time:

v(t) = dx(t)/dt = -A*w*sin(wt + ϕ)

Plugging in t=0, we get:

v(0) = -A*w*sin(0 + ϕ) = 0

This means that sin(ϕ) = 0, which gives us ϕ = 0 or ϕ = π.

Now, we can rewrite the equation for x(t) as:

x(t) = A*cos(wt)

And for the y motion, we can use the same equation with a different phase angle:

y(t) = A*cos(wt + π) = -A*cos(wt) = A*sin(wt)

Therefore, the y motion can be described as A*sin(wt).

I hope this explanation helps you understand the problem better. Keep practicing and you will become more comfortable with solving simple harmonic motion problems!
 

Related to Simple Harmonic motion problems

1. What is Simple Harmonic Motion (SHM)?

Simple Harmonic Motion is a type of periodic motion where the restoring force is directly proportional to the displacement from the equilibrium position and always directed towards it. It is characterized by a sinusoidal or harmonic pattern of motion.

2. What are the factors that affect Simple Harmonic Motion?

The factors that affect Simple Harmonic Motion are the mass of the object, the spring constant, and the amplitude of the oscillations. These factors determine the period and frequency of the motion.

3. How do you calculate the period of a Simple Harmonic Motion?

The period of a Simple Harmonic Motion can be calculated using the formula T = 2π√(m/k), where T is the period, m is the mass of the object, and k is the spring constant.

4. What is the relationship between Simple Harmonic Motion and circular motion?

Simple Harmonic Motion can be thought of as a projection of circular motion onto a straight line. The restoring force in SHM is equivalent to the centripetal force in circular motion, and the displacement from equilibrium is equivalent to the distance from the center in circular motion.

5. How can Simple Harmonic Motion be applied in real-life situations?

Simple Harmonic Motion has many applications in real-life situations such as in pendulum clocks, musical instruments, and shock absorbers in cars. It can also be used in modeling systems with periodic motion, such as the motion of a swinging door or a bouncing ball.

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