Question

show all the work please

5. Solve problems (a) to (c) below. (a) A 60.0-kg block is attached to a massless spring with force constant k = 575 N/m. (1) Find the natural frequency for this simple harmonic oscillator, in Hatz (cycles/sec). (ii) If the amplitude is 0350 m, predict the maximum speed of the block (for Instructor use only) (b) A siren has an intensity of 10W/m²at a distance of 10.0 m away. What is its intensity at a distance of 5.0 m? (BONUS, +5 pts: Translate this intensity to decibels.) (c) A nylon guitar string has a lincar density of 9 50 g/m and its ends are fixed, a distance L = 95.0 cm apart. A 200 Hz oscillator is used to induce standing wave patterns in this string. Find the required tension that produces a standing wave with six antinodes

Answer 1

(a)

(i) Mass attached to the spring = m = 60 kg.

Spring constant = k = 575 N / m.

Hence, angular frequency of oscillation = $\omega$ = $\sqrt{}$ ( k / m ) = $\sqrt{}$ ( 575 / 60 ) rad / s = 3.1 rad / s.

Hence, frequency of the oscillation = f = $\omega$ / 2$\pi$ = ( 3.1 / ( 2 x 3.14 ) ) Hertz = 0.5 Hz.

(ii) Amplitude of the motion is A = 0.35 m.

Hence, the maximum speed of the block is v = A$\omega$ = 0.35 m x 3.1 rad / s = 1.085 m / s.