Simple harmonic motion with an amplitude

In summary, a block of unknown mass is attached to a spring with a spring constant of 5.50 N/m and undergoes simple harmonic motion with an amplitude of 12.5 cm. When the block is halfway between its equilibrium position and the end point, its speed is measured to be 25.0 cm/s. Using the equations Vmax = sqrt(k/m)A, T= 2pi/w, and a_max = kA/m, the mass of the block can be calculated by setting Vmax = 25.0 cm/s and A = 12.5 cm, resulting in m = kA^2/v^2. However, this is incorrect and instead, the total energy of the system should
  • #1
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Homework Statement


A block of unknown mass is attached to a spring with a spring constant of 5.50 N/m and undergoes simple harmonic motion with an amplitude of 12.5 cm. When the block is halfway between its equilibrium position and the end point, its speed is measured to be 25.0 cm/s.

(a) Calculate the mass of the block.
(b) Calculate the period of the motion.
(c) Calculate the maximum acceleration of the block.


Homework Equations


Vmax = sqrt(k/m)A
T= 2pi/w
a_max = kA/m



The Attempt at a Solution


so i thought i would use the first formula i stated to find the mass of the block
but apparently I am wrong.
can someone please help me get started.
thanks
 
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  • #2


Well the total energy of the system is given by 1/2 kA2 and throughout the motion this is interchanged between elastic potential and kinetic energy. So halfway between the max point and equilibrium, how far does the spring stretch? Can you now apply a conservation of energy to get the mass?
 
  • #3


Show your calculations to see where you have made mistake.
 
  • #4


well what i did was
vmax = sqrt(k/m)A
(v^2/A^2)m = k
so
m = kA^2/v^2 but i guess this is wrong

so do i use something like 1/2kA^2 = 1/2mv^2 ?
 

What is simple harmonic motion?

Simple harmonic motion is a type of periodic motion in which an object oscillates back and forth around a central equilibrium point due to the restoring force of a spring or pendulum. It follows a sinusoidal pattern and has a constant period and amplitude.

What is the amplitude in simple harmonic motion?

The amplitude in simple harmonic motion is the maximum displacement of an object from its equilibrium position. It is represented by the letter "A" and is equal to half the distance between the highest and lowest points of the oscillation.

How does amplitude affect simple harmonic motion?

The amplitude affects the energy and velocity of an object in simple harmonic motion. A larger amplitude means a higher maximum velocity and more energy, while a smaller amplitude means a lower maximum velocity and less energy.

What is the relationship between amplitude and frequency in simple harmonic motion?

The relationship between amplitude and frequency in simple harmonic motion is inverse. This means that as the amplitude increases, the frequency decreases and vice versa. This is because the restoring force of the spring or pendulum is directly proportional to the amplitude and inversely proportional to the frequency.

How is simple harmonic motion with an amplitude represented graphically?

Simple harmonic motion with an amplitude is represented graphically as a sinusoidal curve. The amplitude is the height of the curve, and the period is the distance between two consecutive peaks or troughs. The motion is periodic, meaning the curve repeats itself after one full cycle.

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