Question

2) (Ch. 14.1, Equation 14.1) a. Write an equation for the oscillation period in terms of frequency. Define all SI units. b. If an oscillator completes 10 cycles in 5.0 seconds, what are the period and the frequency of the oscillation

Answer 1

a) T = 2 π√ (m / k) c) T = 2 s , f = 0.5 Hz

Step-by-step explanation:

a) In an oscillatory system the angular velocity is

w = √ (k / m)

where w is the angular velocity, k the constant of the spring and m the applied mass

the angular velocity is related to the frequency and the period

w = 2π f

f = 1 / T

w = 2π / T

we substitute

2π / T = √ k / m

T = 2 π√ (m / k)

b) The units If kilograms (m = [kg]) are for the masses, the spring constant is in Newton per meters (k = [N / m], angular velocity in (w = [rad / s]

c) they ask us the period if we have 10 cycles in 5 s

T = 10/5

T = 2 s

f = 1 / T

f = 0.5 Hz