Calculating Amplitude of a Harmonic Motion System with Added Mass

In summary, a particle of mass 4.00 kg attached to a spring with a force constant of 100 N/m is oscillating on a frictionless, horizontal surface with an amplitude of 2.00 m. A 6.00-kg object is dropped on top of the 4.00-kg object while it passes through its equilibrium point and the two objects stick together. The new amplitude of the vibrating system after the collision is 2.00 m. This is found by calculating the angular frequency before and after the impact, as well as the maximum acceleration before and after adding the 6 kg object. The final amplitude is determined by equating the two maximum accelerations.
  • #1
Zynoakib
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Homework Statement


A particle of mass 4.00 kg is attached to a
spring with a force constant of 100 N/m. It is oscillating
on a frictionless, horizontal surface with an amplitude
of 2.00 m. A 6.00-kg object is dropped vertically on top
of the 4.00-kg object as it passes through its equilibrium
point. The two objects stick together. What
is the new amplitude of the vibrating system after the
collision?

Homework Equations

The Attempt at a Solution


Angular frequency before impact adding the block = (100/ 4)^1/2 = 5 s^-1

Angular frequency after impact adding the block = (100/ 10)^1/2 = 3.16 s^-1

Max acceleration before adding the block = Angular frequency^2 x amplitude = 25 x 2 = 50 ms^-2

Force of max acceleration = 50 x 4 = 200N

After addition of the block, the max acceleration will be 200N/ (6 + 4) = 20 ms^-2

Max acceleration after adding the block = Angular frequency^2 x amplitude
20 = 3.16^2 x amplitude
amplitude = 2

I know it is wrong but what is wrong, other than the fact my answer is exactly the same as the old amplitude.
 
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  • #2
Did you do anything with the 'collision' when adding the 6 kg object ?
 
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  • #3
thanks. I have got the answer!
 

FAQ: Calculating Amplitude of a Harmonic Motion System with Added Mass

1. What is Simple Harmonic Motion (SHM)?

Simple Harmonic Motion is a type of movement where an object oscillates back and forth around an equilibrium point. This type of motion is characterized by a sinusoidal pattern and is governed by Hooke's Law, which states that the force applied to an object is directly proportional to the displacement of the object.

2. What is the equation for SHM?

The equation for Simple Harmonic Motion is given by x(t) = A sin(ωt + φ), where x(t) is the displacement of the object at time t, A is the amplitude of the oscillation, ω is the angular frequency, and φ is the phase constant.

3. What factors affect the period of SHM?

The period of Simple Harmonic Motion is affected by the mass of the object, the spring constant, and the amplitude of the oscillation. A larger mass or a stiffer spring will result in a longer period, while a larger amplitude will result in a shorter period.

4. What is the difference between SHM and circular motion?

SHM and circular motion are both types of periodic motion, but they differ in the shape of their paths. In SHM, the object moves back and forth along a straight line, while in circular motion, the object moves around a fixed point in a circular path. Additionally, SHM is caused by a restoring force, while circular motion is caused by a centripetal force.

5. What are some real-life examples of SHM?

Some examples of Simple Harmonic Motion in everyday life include the motion of a pendulum, the vibration of a guitar string, and the motion of a spring. Other examples include the motion of a mass attached to a spring and the motion of a mass hanging from a spring.

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