A support beam, within an industrial building, is subjected to vibrations along its length; emanating from two machines situated at opposite ends of the beam. The displacement caused by the vibrations can be modelled by the following equations. x1 = 3.75 sin (100nt + 2m/9) x2 = 4.42 sin (100nt – 21/5) i State the amplitude, phase, frequency and periodic time of each of these waves. ii. When both machines are switched on, how many seconds does it take for each machine to produce its maximum displacement? Atwhattimedoes eachvibrationfirstreachadisplacementof –2mm? iv. Use the compound angle formulae to expand xland x2 into the form A sin 100mt + B cos 100nt, where A and B are numbers to be found. v. Using your answers from part iv, express x1 + x2 in a similar form. Convert this expression into the equivalent form Rsin(100nt +c).

1. Many structures and materials have what is known as a natural frequency. If we apply a forcing frequency near the natural frequency of a material, the material experiences a phenomenon known as resonance.  This equation models resonance:                                          y(t) + (t/2)cos(t) a) Plot y(t) on the time interval 0 ≤ t ≤ 20.   b) What is the lim as t approaches ∞ y(t)? How do physical objects like a wine glass react to this limit?

A tire has a tread pattern with a crevice every 2.25 cm. Each crevice makes a single vibration as the tire moves. What is the frequency of these vibrations if the car moves at 37 m/s? f=f=  Hz

3: Which of the following describes a standing wave of amplitude 0.5 m, wavelength 2 m and period 32 of amplitude s? (in each, z is in m and t is in s) a: 0.5 sin(x-t/16) b: 0.5 sin(x/16-nt) c: 0.5 sin(x) cos(nt/16) d: 0.5 sin(x/16) cos(nt) e: sin(x) cos(16mt)

a° y(z,t) 1 d*y(x,t) Which of the following wave functions satisfies the wave equation? A.) y(x, t) = A cos(kæ + wt) B.) y(x, t) = A sin(kx +wt) C.) y(x, t) = A[cos(kæ) + cos(wt)] For any of the equations above that satisfy the wave equation what are the transverse velocity and acceleration of a particle at point x?

Figure 6a shows the appearance of a progressive wave transverse wave at a particular instant in time. The wave travels at a speed of 12 ms^-1. All Particles in the wave osciallte with simple harmonic motion.  i. Calculate the frequency and time period of the oscillations. ii. Calculate the maximum acceleration of the particles (magnitude only). iii. Calculate the velocity of the particles when the displacement is ±1.0 cm iv. Compare the amplitude and phase of particles X and Y.

4. For the following, identify the speed of the wave f(x, t) and the direction it is travelling. (a) f(x, t) = 10 cos(10x + 3t) (b) f(x, t) = −2 sin(2x − 4t — π)

A violin string 30.4 cm long with linear density 0.674 g/m is placed near a loudspeaker that is fed by an audio oscillator of variable frequency. It is found that the string is set into oscillation only at the frequencies 1350 and 1800 Hz as the frequency of the oscillator is varied over a certain range. What is the tension in the string? Number i Units

Transversal wave equations that propagate on a rope are Y=20 sin 4π(3t-0,5x)cm .With y and x stated in cm and t in a second. decide amplitude, frequency, wavelength, velocity waves phase, maximum velocity of particles on x=0 inside the rope, The direction the waves creak, How are the equations of particle motion at a balanced position x=0 and determine the curve of the rope on t=0

In the Standing Wave Lab, lab partners Julio and Jose adjust the frequency of a mechanical ocillator to vibrate a 1.70 m length of elastic cord. fixed at both ends, at one of its harmonic frequencies as shown above. The frequency of vibration turns out 79.4 Hz. Determine the speed of the waves in the elastic cord. 21.4 m/s O 54.0 m/s 42.8 m/s 44.5 m/s