Vibrations: A momentum impulse starts a mass into oscillatory motion

[Zamarripa]

Homework Statement

The system shown at rest in fig 1.1(a) could be set into vibration by giving the mass a sudden momentum impulse to the left:by trapping it with a hammer, for example. If the magnitude of the impulse is p1 and its given at time t=0, find (a) the amplitude and (b) the phase constant of the ensuing motion.

Relevant Equations

md^2x/dt^2-kx=0

The fig. 1.1(a) is a mass m attached to a spring that is fixed to a wall. I don't understand what does "a sudden momentum impulse" means. Is it an external force o what?
I imagined that the new equation of motion would be

md^2x/dt^2+dp1/dt-kx=0

md^2x/dt^2+mdv1/dt-kx=0

is this the equation i have to solve?

The problem is from the book Vibrations and Waves in physics from Ian Main.

 

[haruspex]

don't understand what does "a sudden momentum impulse" means

It means going suddenly from rest to moving at some nonzero velocity.

 

[ehild]

Problem Statement: The system shown at rest in fig 1.1(a) could be set into vibration by giving the mass a sudden momentum impulse to the left:by trapping it with a hammer, for example. If the magnitude of the impulse is p1 and its given at time t=0, find (a) the amplitude and (b) the phase constant of the ensuing motion.
Relevant Equations: md^2x/dt^2-kx=0

The fig. 1.1(a) is a mass m attached to a spring that is fixed to a wall. I don't understand what does "a sudden momentum impulse" means. Is it an external force o what?
I imagined that the new equation of motion would be

md^2x/dt^2+dp1/dt-kx=0

md^2x/dt^2+mdv1/dt-kx=0

is this the equation i have to solve?

The problem is from the book Vibrations and Waves in physics from Ian Main.

The '"sudden momentum impulse" certainly means that the mass is given momentum by a sudden impulse p1 at t=0. Except for the initial moment, there is no external force.
What is the initial velocity of the vibration then?
Check the relevant equation, it is not correct.

 

[Zamarripa]

The '"sudden momentum impulse" certainly means that the mass is given momentum by a sudden impulse p1 at t=0. Except for the initial moment, there is no external force.
What is the initial velocity of the vibration then?
Check the relevant equation, it is not correct.

The initial velocity is v1=p1/m and the problem is just a simple harmonic oscillation with initial conditions x(t=0)=x₀, v(t=0)=v₁?

 

[haruspex]

The initial velocity is v1=p1/m and the problem is just a simple harmonic oscillation with initial conditions x(t=0)=x₀, v(t=0)=v₁?

Yes.