1. A string vibrates in its 3rd harmonic standing wave pattern. The mass and length of the string are given. Also given is the tension in the string and the transverse velocity of the string at the antinode located at x = Length/2 when the standing wave has no displacement at t = 0.00s
M = 1.80g, L = 90.0cm, T = 45.0 N, Vy0 = 1.25ms-1 at Length/2 at t = 0.00s.
The questions asked me to find the wavelength, speed of the wave, frequency in the string. I found these already. wavelength is 0.6m, speed is 150m/s, and frequency is 250Hz.
But the question I was not able to do is this one:
* Determine the second time after t = 0.00s that the transverse force in the string located at x = 0.250m is 0.250N ˆj. (force of string at x on the string to its right).
2. Velocity at antinode is 1.25m/s, so i think 2Asin(kx)sin(wt) or just 2Asin(kx) should be important because I guess need to find the amplitude which I couldn't do. Transverse Force F = KAFsin(kx - wt) could be useful too I guess.
3. I tried using the forrmula 2Asin(kx)sin(wt) to find amplitude and then use F = KAFsin(kx - wt) to find the time the question is asking for I'm getting some big numbers and the calculator is giving errors.