Q2) Assuming that the wave on a string is represented by 2 = yo sin--(st-x) r y(

Question

Q2) Assuming that the wave on a string is represented by 2 = yo sin--(st-x) r y(x, t) y(x, t) = yo sin (M-X) where y is the tra nsverse displacement attimet (sec) of the piece of string atx (m)·Yosandlambda, are all constants. Find the velocity and acceleration of the small piece of string at x = 10 m as a function of time. Making use of the fact that the piece of string satisfies Newton's Second Law, show that the piece of string is acted on by a Hooke's Law force. (i.e. a force that can be written in the same form as the restoring force from an ideal spring)

Explanation / Answer

Y(x,t) = y0 sin (k(x-st)) k = 2pi/lambda

x = 10 m

y(10,t ) = y0 sin (k(10-st)

V= dy/dt = -ksy0cos(k(10-st))

a= dv/dt = - (ks)^2y0sin(k(10-st))

F = ma = - m(ks)^2y0sin(k(10-st)) = = -m(ks)^2y

the force has the form of F = -Ky, where K = m(ks)^2, and obey Hook'slaw.

Related Questions

Navigate

• Browse (All)
• Browse Q
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.