Amplitude of a simple harmonic motion equation

In summary, the equation for calculating the amplitude of a simple harmonic motion is A = xmax - xmin. The amplitude and period of a simple harmonic motion are inversely related according to the equation T = 2π√(m/k). The amplitude of a simple harmonic motion remains constant throughout the motion and does not affect the total energy of the system. If the amplitude is equal to zero, the motion becomes stationary and there is no oscillation.
  • #1
nehcrow
15
0
if you have the equation: x(t) = Acos(ωt + ϕ)

and you have the following information: A 200 g block hangs from a spring with spring constant 10 N/m. At t = 0s the block is 20 cm below the equilibrium position and moving upward with a speed of 100 cm/s.

The answers give a short method of calculating the amplitude but I have no idea how the reached it, basically what they did was: A = sqrt((x0)^2 + (v0/ω)^2)
how did they reach that conclusion??
 
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  • #2
velocity v = dx/dt = -Aωsin(ωt + φ)
Square both the sides and simplify.
 
  • #3
Thanks!
 

Related to Amplitude of a simple harmonic motion equation

1. What is the equation for calculating the amplitude of a simple harmonic motion?

The equation for calculating the amplitude of a simple harmonic motion is A = xmax - xmin, where xmax is the maximum displacement from equilibrium and xmin is the minimum displacement from equilibrium.

2. How is the amplitude of a simple harmonic motion related to the period?

The amplitude and period of a simple harmonic motion are inversely related. This means that as the amplitude increases, the period decreases, and vice versa. This relationship is described by the equation T = 2π√(m/k), where T is the period, m is the mass, and k is the spring constant.

3. Can the amplitude of a simple harmonic motion change over time?

No, the amplitude of a simple harmonic motion remains constant throughout the motion. This is because the amplitude is determined by the initial conditions of the system, such as the starting position and velocity.

4. How does the amplitude affect the energy of a simple harmonic motion?

The amplitude of a simple harmonic motion does not affect the total energy of the system. The total energy is determined by the mass and spring constant, and remains constant throughout the motion.

5. What happens if the amplitude of a simple harmonic motion is equal to zero?

If the amplitude of a simple harmonic motion is equal to zero, the motion becomes a stationary point and there is no oscillation. This means that the object will remain at rest at the equilibrium position.

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