Answer:
a) 0.328 Hz b) 73 cm (0.73 m)
Explanation:
Using law of conservation of momentum:
M1U1 + M2U2 = V(M1+M2) since the mass stuck together. where M1 is the mass 20 kg travelling with the U1 speed 3m/s and M2 is the 20kg at rest with U2 = 0 and V is the final speed of the mass after collision.
substitute the values into the equation
20 × 3 + 20 ×0 = V (20+20)
V = 60 / 40 = 1.5 m/s
The period of the oscillation can be calculated with the formula:
T = 2π√ ( m/k) where T is the period in seconds and F is the frequency of the oscillation
substitute the values into the formula
T = 2×3.142×√ (40/170) = 3.05s
T = 1/F
F = 1/T = 1/ 3.05 = 0.328Hz
b) The amplitude of the oscillation can calculated using the formula
V = x√(K/m) where x is the amplitude in cm and V is the maximum speed that caused the displacement (amplitude) x
substitute the values into the formula
1.5 = x × √ (170/40) = x × 2.062
divide both side by 2.062
x = 1.5 / 2.062 = 0.73m = 0.73 cm
