Finding Amplitude of a Mass on a Spring | Simple Harmonic Motion

In summary, the problem involves a 12.5 kg mass attached to a 1e^5 N/m spring, causing oscillation with an initial position of 4.9 cm and initial velocity of 8.64 m/s. The amplitude and phi of the oscillation are found, and the position at a specific time is being calculated using these values. The resulting position is 6.993 cm, but the system is indicating an error.
  • #1
ultrapowerpie
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Simple Harmonic Motion- Spring problem

Homework Statement



A 12.5 kg mass is suspended on a 1e^5 N/m spring. The mass oscillates up and down from the equilibrium position
[tex]y(t)= Asin(wt+\phi)[/tex]

Find the amplitude of the oscillating mass

Initial position- 4.9 cm
Initial velocity= +8.64 m/s
Time= 0

Homework Equations


No idea, see below


The Attempt at a Solution


Ok, I found the frequency, which is 89.44 1/s. But, I don't know how to figure out the amplitude of this thing with the information given. I've looked, and I can't find a formula to use. If someone could show me what formula I'm supposed to use, it would be greatly appreciated.
 
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  • #2
Ok, I figured out the amplitude and the phi. But, here's the latest part of the question

Calculate teh position @ t=.0149 seconds

If A=10.83 cm
w= 89.44 (1/s)
Phi= 26.895 degrees

Plugging that into the equation, I get 6.993, yet the system says it's wrong. It also says to answer in cm, but I'm not seeing any discrepencies here. >.>
 
  • #3


As a scientist, it is important to understand the principles and equations involved in the problem before attempting to find a solution. In this case, the problem deals with simple harmonic motion, which is defined by the equation y(t)=Asin(wt+ϕ). This equation represents the position of the mass at a given time, where A is the amplitude, w is the angular frequency, t is time, and ϕ is the phase angle.

In order to solve for the amplitude, we need to first understand the given information. The mass, m, is 12.5 kg and the spring constant, k, is 1e^5 N/m. From this, we can calculate the angular frequency, w, using the equation w=√(k/m). Plugging in the values, we get w=√(1e^5/12.5)≈89.44 rad/s.

Next, we can use the initial position and velocity to solve for the phase angle, ϕ. Since the mass starts at a position of 4.9 cm, we can write y(0)=4.9 cm=Asin(0+ϕ), which simplifies to ϕ=0. Similarly, we can use the initial velocity to solve for the amplitude. Plugging in the values, we get +8.64 m/s=A(89.44 rad/s)cos(0), which simplifies to A≈9.68 cm.

Therefore, the amplitude of the oscillating mass is approximately 9.68 cm. It is important to note that the units for the amplitude will be the same as the units for the initial position and velocity. In this case, they are all in units of length.

In conclusion, understanding the principles and equations involved in the problem allowed us to solve for the amplitude of the oscillating mass. As a scientist, it is important to have a strong foundation in the fundamentals of physics in order to solve complex problems like this one.
 

What is Simple Harmonic Motion?

Simple Harmonic Motion (SHM) is a type of periodic motion in which an object oscillates back and forth around an equilibrium point, following a sinusoidal pattern. It occurs when there is a restoring force that is directly proportional to the displacement of the object from its equilibrium position.

What are the factors that affect the frequency of Simple Harmonic Motion?

The frequency of SHM is affected by two main factors: the mass of the object and the stiffness of the system. A heavier mass will result in a lower frequency, while a stiffer system will have a higher frequency. The length of the pendulum, the spring constant, and the gravitational acceleration can also affect the frequency.

What is the equation for Simple Harmonic Motion?

The equation for SHM is given by x(t) = A*cos(ωt), where x(t) is the displacement of the object at time t, A is the amplitude of the motion, and ω is the angular frequency. This equation describes the sinusoidal motion of the object as it oscillates back and forth.

What is the difference between Simple Harmonic Motion and Damped Harmonic Motion?

In Simple Harmonic Motion, there is no external force acting on the system, and the amplitude remains constant. In Damped Harmonic Motion, there is an external force (such as friction) that causes the amplitude to decrease over time. This results in the oscillations becoming smaller and eventually stopping.

What are some real-life examples of Simple Harmonic Motion?

Some common examples of Simple Harmonic Motion include a pendulum, a mass-spring system, and a vibrating guitar string. Other examples include the motion of a swing, a bouncing ball, and a tuning fork. In nature, the motion of a leaf on a tree branch and the motion of a fish swimming are also examples of SHM.

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