What is the phase of the SHM at that point

In summary, the conversation discusses a mass attached to a spring on a frictionless surface and its motion as it is pulled and released. The speed of the mass at a point where the spring is compressed by 0.05 m is 0.866 m/s, and the phase of the Simple Harmonic Motion (SHM) at that point is 120° relative to a phase of zero at the time of release. The solution for part a is obtained using the equation V = ω √ (A2 - y2) where A is the amplitude, ω is the angular frequency, and y is the displacement from the equilibrium position. For part b, the answer is found using the equation cosωt, suggesting a
  • #1
Voltrical
11
0

Homework Statement



A mass is attached to a spring on a frictionless horizontal surface. The mass is pulled to stretch the spring by 0.1 m, & then gently released. A short time later, as the mass passes through the equilibrium position, its speed is 1 m/s.

Part a)

What is the speed of the mass at the point where the spring is compressed by 0.05 m?

Part b)

What is the phase of the SHM at that point, relative to a phase of zero at the time of release?

Homework Equations



The Attempt at a Solution



Part a)

A = 0.1 m
ωA =1 m/s
ω = 1 / 0.1 = 10 rad/s
y = 0.05 m
V = ω √ (A2 - y2)
= 10 * [ √ ( 0.01 - 0.0025 ) ]
= 0.866 m/s, this answer is correct because my teacher gave us the answer.

Part b)

Answer = 120°, how to get this answer?
 
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  • #2
Hi Voltrical! :smile:
Voltrical said:
Part b)

Answer = 120°, how to get this answer?

shm is amplitude times cosωt …

so won't it have something to do with cos120° ? :wink:
 

Related to What is the phase of the SHM at that point

What is the phase of the SHM at that point?

The phase of SHM (simple harmonic motion) at a point is the measure of the position of an object in its cycle of oscillation. It is usually represented by the angle between the object's starting position and its current position.

How is the phase of SHM determined?

The phase of SHM is determined by the initial conditions of the motion, such as the amplitude and the initial displacement of the object. These conditions are used to calculate the phase angle using trigonometric functions.

What is the relationship between phase and frequency in SHM?

In SHM, the phase and frequency are inversely proportional. This means that as the frequency increases, the phase decreases and vice versa. This relationship follows the equation: phase = 2π x (frequency x time).

Can the phase of SHM change over time?

Yes, the phase of SHM can change over time. As the object continues to oscillate, the phase angle will increase or decrease depending on the frequency and time elapsed. The phase will reset to its original value after one full cycle of oscillation.

How is the phase of SHM used in real-life applications?

The phase of SHM is used in various real-life applications, such as in measuring the vibrations of structures, tuning musical instruments, and creating wave patterns in electronics. It is also used in studying the behavior of waves and predicting their interactions with different materials.

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