A transverse wave on a string is described by the expression: y = (0.12m)sin(pix

Question

A transverse wave on a string is described by the expression: y = (0.12m)sin(pix/8 + 4 pit) (a) Determine the transverse speed and acceleration of the string at t = 0.200s for the point on the string located at x = 1.60 m. (b) If the displacement of the wave at x = 0, t = 0, would be 1 m, then what will be initial phase, 0.99 radians 4. A mass of 0.5 kg connected to a light spring of force constant 20 N/m oscillates on a horizontal, frictionless surface. (a) Calculate the total energy of the system and the maximum speed of the mass if the amplitude of the motion is 3 cm. Compute the kinetic and potential energies when the displacement equals 2 cm, 9 times 10^-3 J, 0.19, 5 times 10^-3 J

Explanation / Answer

3)   a) transverse speed = (0.12 * 3.14 * 4) * cos(pi)   =   - 1.507 m/sec

             acceleration   =   - (0.12 * 3.14 * 4 * 3.14 * 4) * sin(pi)   =   0   m/sec2

      b)   Initial phase =   sin-1(0.1/0.12)

                              =    0.99 radians

4)   a)   total energy of system = 1/2 * k * A2

                                             =    0.5 * 20 * 0.03 * 0.03   =    9 * 10-3 J

     => maximum speed of mass = 0.03 * sqrt(20/0.5)

                                                    =    0.189 m/sec

   Kinetic energy =   9 * 10-3 * 0.672 = 4 * 10-3 J

   Potential energy = (9 * 10-3) - (4 * 10-3) =    5 * 10-3 J

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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