Simple Harmonic Motion II

  1. A 5.0 kg object is dropped on a vertical spring from a height of 2.0m. If the maximum compression of the spring is 40 cm, what is its force constant ?

    2. Energy conservation

    mgh = ½kx2

    k = 2mgh/x2 = (2 x 5 x 9.8 x 2.4)/(0.4)2 = 1470 N/m



  2. A 100 g mass is suspended from a spring whose force constant is 50 N/m. The mass is then pulled down 10mm and released. What is the amplitude of the resulting oscillations ? What is their frequency ?

    3. Amplitude = 10 mm

    f = (1/T) = (1/2π)(k/m)½ = (1/2π)(50/0.1)½ = 3.56 Hz



  3. An object of unknown mass is suspended from a spring and the system is set in oscillation. If the frequency of the oscillations is 2.0 Hz, by how much did the spring stretch when the object was suspended from it ?

    4. f = (1/T) = (1/2π)(k/m)½

    k = (2πf)2m

    but, FR = kx = mg

    therefore x = mg/k = mg/((2πf)2m) = g/(4π2f2) = 10/(4π2 x 4) = 0.0625 m = 6.25 cm