Write an equation for the position of the cart as a function of time using the given quantities above. b) Write an equation for the frequency heard by a stationary observer standing to the right of the track as a function of time. c) If the maximum sound level heard by the person is 75 decibels when the speaker is at its closest distance 1.00 m from him, what is the minimum sound level heard by the observer in decibels

(a). w / 2π = 1/2π * (√k + ky/m).

(b). Vi / (Vi + Aw sin wt) or Vi / (Vi - Aw sin wt).

(c). 68.97 dB.

Explanation:

We are given that the two springs constant = k and ky respectively, mass = m.

So, k which is the left hand spring is stretched to the right and ky which is the right hand spring is stretched to the left. Thus, we will have;

Total force = - (k + ky) ∆x. Where ∆x = displacement.

So, total force = displacement.

Thus, mw^2 ∆x = (k + ky) ∆x.

w^2 = (k + ky) / m.

Therefore, the frequency,

= w / 2π = 1/2π * (√k + ky/m).

(b). In simple harmonic motion, the displacement, x (t) = A cos (wt).

Therefore, the velocity = dx (t) / dt = - Aw sin wt.

Hence, the frequency heard:

= Vi / (Vi + Aw sin wt) or Vi / (Vi - Aw sin wt).

(C). Minimum intensity = (4π * maximum intensity) / 4π * (2) ^2.

= Maximum intensity / 4.

Hence, the intensity level, y = 10 log I (min) / I (h).

= 10 log (0.79 * 10^7).

= 68.97 dB.