Finding Force and Distance in Simple Harmonic Motion Problem

In summary, for a system consisting of a suspended box of mass M and a small block of mass m inside, pulled down by a distance d and released from rest, the force between the bottom of the box and the block can be determined using the equation F(m+M)=mg+ma. The value of d at which the block just begins to leave the bottom of the box during vertical oscillations can be found by solving for x(t) in the equation x(t)=dcos(ωt), where ω=√(k/(m+M)).
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Kefurinu
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Homework Statement


A box of mass M is suspended by a spring of stiffness k. A small block of mass m is placed inside the box. If the system is pulled downward by a distance d and then released from rest:

a.) find the force between the bottom of the box and the block as a function of time;
b.) for what value of d does the block just begin to leave the bottom of the box at the top of the vertical osscilations?


Homework Equations


F(m+M)=mg+ma
x(t)=dcos(ωt)
ω=√(k/(m+M)).


The Attempt at a Solution


I'm unsure of how to proceed to determine the force of reaction from the equations above that I've worked out.
 
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Related to Finding Force and Distance in Simple Harmonic Motion Problem

1. What is Simple Harmonic Motion?

Simple Harmonic Motion is a type of periodic motion in which an object moves back and forth in a straight line due to a restoring force that is directly proportional to the displacement from the object's equilibrium position. This type of motion is commonly seen in oscillating systems such as a pendulum or a mass-spring system.

2. What is the equation for Simple Harmonic Motion?

The equation for Simple Harmonic Motion is x = A*cos(ωt + φ), where x is the displacement from equilibrium position, A is the amplitude, ω is the angular frequency, and φ is the phase angle. This equation describes the position of the object at any given time during its oscillation.

3. What is the relationship between period and frequency in Simple Harmonic Motion?

The period of Simple Harmonic Motion is the time taken for one complete oscillation, while the frequency is the number of oscillations per unit time. The two are inversely proportional, meaning that as the frequency increases, the period decreases, and vice versa.

4. What factors affect the period of Simple Harmonic Motion?

The period of Simple Harmonic Motion is affected by the mass of the object, the spring constant of the system, 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.

5. How is Simple Harmonic Motion related to energy conservation?

In Simple Harmonic Motion, the total mechanical energy of the system (kinetic energy + potential energy) remains constant. This is because the restoring force is conservative and does not dissipate energy. As the object oscillates, the energy is constantly exchanged between kinetic and potential energy, but the total energy remains the same.

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