A. A mass oscillates at a frequency of 3 Hz and an amplitude of 4 cm. What is it

Question

A. A mass oscillates at a frequency of 3 Hz and an amplitude of 4 cm. What is its position at time t = 0 and time t = 2.67 s?

Position (t=0 s) =  centimeters

Position (t=2.67 s) =  centimeters

B. A body makes 2 complete oscillations in 4 seconds. What is its acceleration when it is displaced a distance of x = +3 cm from its equilibrium position?

Acceleration =  m/s2

C. A car and its passengers have a total mass of 1,800 kg. The car is supported by four springs, each having a constant of 11,000 N/m. What is the frequency of vibration when the car hits a bump in the road?

Frequency =  Hertz

D. What is the speed of sound in air (M = 29 g/mol and gamma = 1.4) on a day when the tempearture is 35 degrees?

Sound Speed = m/s

Explanation / Answer

here,

Part A:
frequency, f = 3 Hz
amplitude, a = 4 cm

Angular frequency, w = 2*pi*f = 2*pi*3 = 18.849 rad/s

Position in shm is given as,
x = a*Sin(w*t)

position at t = 0

x = 4*sin(0)
x = 0

position at t = 2.67
x = 4*sin(18.849 * 2.67)
x = 0.245 cm

Part B:
frequency, f = 1/4 = 0.25 Hz
displacement, x = 3 cm = 0.03 m

acceleration ion shm, a = -(2*pi*f)^2 * x ( s is displacement)
a = -(2*pi*0.25)^2 * 0.03
a = - 0.0740 m/s^2

Part C:
frequency in shm is given as, f = 1/(2pi) * Sqrt(k/m) ( k is spring constant, m is mass)
f = 1/(2pi) * Sqrt(11000/1800)
f = 0.394 Hz

Part D:
Speed of sound , v = sqrt( (gamma * gas consatant * Temp of medium )/ Molecular mass of gas )
under given standard conditioc above expression si reduced to form, v = 20.05 * sqrt(T)

Where Temperature is in Kelvins

v = 20.05*sqrt(35 + 273.15)

v = 351.986 m/s

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