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

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

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

  distance on the y-axis and time on the x-axis.

explanation:

the instantaneous velocity = change in position/time taken

the slope of the graph should give instantaneous velocity.

  slope of a graph = change in value of y -axis / change in values of x -axis

  comparing both the equations

    change in value of y -axis = change in position

  change in values of x -axis = time taken

so position values should be on the y axis and time values should be on the x axis.

distance on the y-axis and time on the x-axis.