# Simple harmonic oscillation question

• sapiental
In summary, the displacement of a simple harmonic oscillator can be described by the function x = Asin(wt + phi). To find the speed when the displacement is sqrt(3) A/2, the answer is piA/2. However, the formula for velocity at point x is v_x_ = -wAsin(wt + phi) and it may be difficult to associate position x with speed. Conservation of energy can be used to find the velocity by plugging in x. Additionally, a diagram shows that T = 2s. The formula for velocity is v_x_ = +-w sqrt(A^2 - x^2) and can be derived using conservation of energy.
sapiental
the displacement of a simple harmonic oscillator versus time is
described by the function x = Asin(wt + phi)

find the speed when the displacement is sqrt(3) A/2

the answer is piA/2 but I have no idea how the professor got it...

the function for the velocity at point x in our book is

v_x_ = -wAsin(wt + phi)

for some reason it is hard for me to associate the position x with the speed... is there a formula that gives the velocity by just plugging in x?

I just also found a diagram that gives T = 2s which I didn't see before

Last edited:
Hint -- Try to use conservation of energy.

ohhhh right

v_x_ = +-w sqrt(A^2 - x^2)

I got it from here, thanks alot!

## 1. What is simple harmonic oscillation?

Simple harmonic oscillation is a type of periodic motion in which an object oscillates back and forth around an equilibrium point due to a restoring force that is proportional to the displacement from the equilibrium point. This type of motion is characterized by a sinusoidal curve.

## 2. What are the factors that affect simple harmonic oscillation?

The factors that affect simple harmonic oscillation include the mass of the object, the stiffness of the spring or restoring force, and the amplitude (maximum displacement) of the oscillation. The period (time for one complete oscillation) is not affected by these factors and remains constant.

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

Simple harmonic oscillation differs from other types of oscillations in that it follows a specific mathematical relationship between the restoring force and the displacement, known as Hooke's Law. This means that the oscillation is always periodic and the period is independent of the amplitude of the oscillation.

## 4. What is the equation for simple harmonic oscillation?

The equation for simple harmonic oscillation is x = A cos(ωt), where x is the displacement from equilibrium, A is the amplitude (maximum displacement), ω is the angular frequency (related to the period), and t is the time. This equation can also be written as x = A sin(ωt) depending on the starting point of the oscillation.

## 5. How is simple harmonic oscillation used in real-life applications?

Simple harmonic oscillation has many real-life applications, such as in pendulum clocks, musical instruments, and shock absorbers. It is also used in many engineering and physics applications, such as in the study of waves and vibrations, and in the design of precision instruments.

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