Answer:
Therefore, the spring constant of each spring = 1.6 × 10⁻⁶ kg/s².
Explanation:
The period (T) of a spring in oscillation = 2π √(m/k)............. equation 1
Where m = mass acting on the spring (kg), k = spring constant of the spring (kg/s²).
Making k the subject of equation 1
k = T²/(4π²×m) .......................... equation 2
From the question, F = 4.42 Hz,
since T = 1/F
then, T = 1/F = 1/4.42 =0.226 s, π = 3.143
since the weight of the mass is evenly distributed over the four identical spring, Hence
m = 1450/4 = 362.5 kg
Substituting these values into equation 2
k = 0.226/{(4×3.143²)362.5}
k = 0.226/(14323.751)
k = 0.0000016 kg/s²
k = 1.6 × 10⁻⁶ kg/s².
Therefore, the spring constant of each spring = 1.6 × 10⁻⁶ kg/s².
