Respuesta :
we obtain v0 =−xm ωsinϕ=3.06m/s.
What is harmonic motion?
When the restoring force is proportionate to the displacement but acting in the opposite direction, an oscillating mass moves in a manner known as harmonic motion. The sine wave has a constant frequency and amplitude and can be used to describe harmonic motion because it is periodic.
What is mass?
The amount of matter in a particle or object is represented by its mass, which is denoted by the symbol m. In the International System (SI), the kilogram serves as the default unit of mass (kg).
ω= mK = 2.00kg/10100Nm
=7.07rad/s.
Energy methods provide one method of solution. Here, we use trigonometric techniques based on Eq. x=x m cos(ωt+ϕ) and Eq. v=−ωx
msin(ωt+ϕ).
(a) Dividing Eq. v=−ωxm
sin(ωt+ϕ) by Eq.x=xmcos(ωt+ϕ), we obtain
xv=−ωtan(ωt+ϕ)
So that the phase (ωt+ϕ) is found from ωt+ϕ=tan−1( ωx−v )=tan −1( (7.07rad/s)(0.129m)
−3.415m/s).
With the calculator in radians mode, this gives the phase equal to –1.31rad. Plugging this back into Eq.x=xmcos(ωt+ϕ), leads to 0.129m=xmcos(−1.31) ⇒xm=0.500m.
(b) Since ωt+ϕ=–1.31rad at t=1.00s, we can use the above value of ω to solve for the phase constant ϕ. We obtain ϕ=–8.38rad (though this, as well as the previous result, can have 2π or 4π (and so on) added to it without changing the physics of the situation). With this value of ϕ, we find x0=xmcosϕ=−0.251m.
(c) And we obtain v0 =−xm ωsinϕ=3.06m/s.
Therefore, we obtain v0 =−xm ωsinϕ=3.06m/s.
Learn more about simple harmonic motion from the given link.
https://brainly.com/question/2195012
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