# Simple harmonic motion, help please

• Ayrity
In summary, an air-track glider attached to a spring oscillates with a period of 1.50 seconds and starts at 5.40 cm left of equilibrium position with a velocity of 39.2 cm/s to the right. The question is asking for the phase constant in the equation x=A*cos(wt+Fi original) with a range of -Pi rad < Fi original < Pi rad. Guidelines for posting in the forum can be found at https://www.physicsforums.com/showthread.php?t=28.

#### Ayrity

An air-track glider attached to a spring oscillates with a period of 1.50 seconds At t=0 the glider is 5.40 cm* left of the equilibrium position and moving to the right at 39.2*cm/s.

What is the phase constant , if the equation of the oscillator is taken to be x=A*cos(wt+Fi original) ? Give an answer in the range -Pi rad<Fi Original<Pi rad.

This question is stumping the hell out of me haha, any help would be appreciated, thanks guys

In the formula you have, what numbers can you plug in ? Also, what do you intend to do about the velocity that you are given ?

The phase constant, denoted as Φ or ϕ, represents the initial phase or starting position of the oscillating object. In simple harmonic motion, the phase constant is the angle at which the object starts its motion relative to the equilibrium position.

In this case, we can use the given information to find the phase constant. We know that the glider is 5.40 cm to the left of the equilibrium position at t=0 and is moving to the right at 39.2 cm/s. This means that the glider is at its maximum displacement and moving towards the equilibrium position. This corresponds to the point where the cosine function is at its maximum value, which is when the argument of the cosine function is equal to 0.

Using the given equation x=A*cos(wt+Φ), we can set the argument of the cosine function to 0 and solve for Φ.

0=A*cos(0+Φ)

Since the cosine of 0 is equal to 1, we can simplify the equation to:

0=A*cos(Φ)

Since we know that the glider is at its maximum displacement, we can set A=5.40 cm. Therefore, the equation becomes:

0=5.40*cos(Φ)

Solving for Φ, we get:

Φ=arccos(0/5.40)

Φ=arccos(0)

Φ=0

Therefore, the phase constant in this case is 0 radians. This means that at t=0, the glider is at its maximum displacement to the left of the equilibrium position and is moving towards the equilibrium position.

Hope this helps!

## 1. What is simple harmonic motion?

Simple harmonic motion is a type of periodic motion in which a body or object moves back and forth in a repetitive pattern along a straight line, with its maximum displacement equal to its amplitude and its velocity and acceleration following a sinusoidal curve.

## 2. What are the principles behind simple harmonic motion?

The principles behind simple harmonic motion are based on Hooke's Law, which states that the force exerted by a spring is directly proportional to its displacement from its equilibrium position. This means that the greater the displacement, the greater the restoring force and the greater the acceleration, resulting in a sinusoidal motion.

## 3. How is simple harmonic motion different from other types of motion?

Simple harmonic motion is different from other types of motion because it is a purely linear motion, meaning it occurs along a straight line. It also follows a specific pattern of displacement, velocity, and acceleration that is determined by the amplitude and frequency of the motion.

## 4. What are the applications of simple harmonic motion?

Simple harmonic motion has many applications in the fields of physics, engineering, and mathematics. It can be used to model the motion of pendulums, springs, and other oscillating systems. It is also used in the design of mechanical systems, such as shock absorbers and tuning forks.

## 5. How is simple harmonic motion related to oscillation and resonance?

Simple harmonic motion is a type of oscillation, which is the repetitive motion of a body or object around an equilibrium point. Resonance occurs when an external force is applied to a system at its natural frequency, resulting in an increase in amplitude of the oscillations. Simple harmonic motion can exhibit resonance when the external force is applied at the same frequency as the natural frequency of the system.