Simple Harmonic Motion with Impulse

In summary: This momentum will cause the mass to oscillate around its equilibrium position. The amplitude of this oscillation will depend on the initial velocity given by the impulse. The equation for the displacement of the mass from its initial position at time t can be expressed as x=asin(ωt), where a is the amplitude and ω is the angular frequency. The angular frequency can be found using the mass, spring constant, and natural length of the spring. Therefore, in summary, the equation for x in terms of t can be written as x=asin(ωt), where a is the amplitude and ω is the angular frequency determined by the mass, spring constant, and natural length of the spring.
  • #1
conorordan
13
0

Homework Statement



A particle P of mass 0.6kg is attached to one end of a light elastic spring of modulus of elasticity 72N and natural length 1.2m.
The other end of the spring is fixed to a point A on the smooth horizontal table on which P rests. Initially P is at rest and is 1.2m from A.
The particle receives an impulse of 3Ns in the direction AP.
Given that t seconds after the impulse the displacement of P from its initial position is x metres.

Find an equation for x in terms of t

Homework Equations



Tension in a spring, [itex]T = \frac{\lambda x}{l}[/itex]

The Attempt at a Solution



I know the answer will be in the form x=asin(ωt) and I am competent with finding the period etc but it is the impulse that is throwing me off.
 
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  • #2
conorordan said:

Homework Statement



A particle P of mass 0.6kg is attached to one end of a light elastic spring of modulus of elasticity 72N and natural length 1.2m.
The other end of the spring is fixed to a point A on the smooth horizontal table on which P rests. Initially P is at rest and is 1.2m from A.
The particle receives an impulse of 3Ns in the direction AP.
Given that t seconds after the impulse the displacement of P from its initial position is x metres.

Find an equation for x in terms of t

Homework Equations



Tension in a spring, [itex]T = \frac{\lambda x}{l}[/itex]

The Attempt at a Solution



I know the answer will be in the form x=asin(ωt) and I am competent with finding the period etc but it is the impulse that is throwing me off.
The impulse will give the mass an (almost) instant momentum.
 

1. What is Simple Harmonic Motion with Impulse?

Simple Harmonic Motion with Impulse refers to the oscillatory motion of an object due to an external force acting on it for a short period of time. It is a combination of the two types of motion - simple harmonic motion and impulse motion.

2. What is the formula for calculating Simple Harmonic Motion with Impulse?

The formula for calculating Simple Harmonic Motion with Impulse is given by x = A cos(ωt) + B sin(ωt) + Jt, where x is the displacement of the object, A and B are constants, ω is the angular frequency, t is the time, and J is the impulse applied to the object.

3. How is Simple Harmonic Motion with Impulse different from Simple Harmonic Motion?

Simple Harmonic Motion with Impulse is different from Simple Harmonic Motion because it involves the application of an external force for a short period of time, whereas Simple Harmonic Motion does not require an external force to maintain the oscillations.

4. What is the significance of Simple Harmonic Motion with Impulse?

Simple Harmonic Motion with Impulse is significant because it can be used to model real-life situations, such as a pendulum being pushed by a person or a spring being hit by a hammer. It also helps in understanding the behavior of systems that experience both oscillatory and impulse forces.

5. How is Simple Harmonic Motion with Impulse applied in physics and engineering?

Simple Harmonic Motion with Impulse has various applications in physics and engineering, such as in the design of shock absorbers, tuning of musical instruments, and analysis of earthquake vibrations. It is also used in studying the behavior of electrical circuits and mechanical systems.

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