Examination Style Questions 7 from Oscillations note

The apparatus of Fig. 13.16 is used to demonstrate forced vibrations and resonance. A 50 g mass is suspended from the spring, which has a spring constant of 7.9 N m⁻¹.

a)  Calculate the resonant frequency f₀ of the system.

b)  A student suggests that resonance should also be observed at a frequency of 2 f₀. Discuss this suggestion.

Solution:

a)

b) If the driving frequency is increased further, the amplitude of oscillation of the mass decreases.

Reference: Examination Style Questions 7 from note

Examination Style Questions 5 from Oscillations note

One particle oscillating in simple harmonic motion has ten times the total energy of another particle, but the frequencies and masses are the same. Calculate the ratio of the amplitudes of the two motions.

Solution:

Reference: Examination Style Questions 5 from Oscillations note

Examination Style Questions 2 from Oscillations note

A particle is oscillating in simple harmonic motion with frequency 50 Hz and amplitude 15 mm. Calculate the speed when the displacement from the equilibrium position is 12mm.

Solution:

Reference: Examination Style Questions 2 from note

Examination Style Questions 1 from Oscillations note

A particle is oscillating in simple harmonic motion with period 4.5ms and amplitude 3.0cm. At time t = 0, the particle is at the equilibrium position. Calculate, for this particle: 

a)the frequency,
b)the angular frequency,
c)the maximum speed,
d)the magnitude of the maximum acceleration,
e)the speed at time t = 1.0 ms.

Solution:

Reference: Examination Style Questions 1 from Oscillations note

Tough Question 1 (Chapter: Production and use of ultrasound in diagnosis)

A parallel beam of ultrasound passes through a thickness of 4.0 cm of muscle. It is then incident normally on a bone having a specific acoustic impedance of 6.4 × 106 kg m−2 s−1. The bone is 1.5 cm thick. Using data from Table 14.2, calculate the fraction of the incident intensity that is transmitted through the muscle and bone.

Table 14.2 Some values of linear absorption (attenuation) coefficient for ultrasound

Solution: