Answer:
24958.764 N/m
Step-by-step explanation:
From the question given above, the following data were obtained:
Mass (m) = 1405 kg
Frequency (f) = 0.669 s¯¹
Spring constant (K) =?
Next, we shall determine the period. This can be obtained as follow:
Frequency (f) = 0.669 s¯¹
Period (T) =?
T = 1/f
T = 1/0.669
T = 1.49 s
Finally, we shall determine the spring constant. This can be obtained as follow:
Mass (m) = 1405 kg
Period (T) = 1.49 s
Pi (π) = 3.14
Spring constant (K) =?
T = 2π√(m/K)
1.49 = 2 × 3.14 × √(1405/K)
1.49 = 6.28 × √(1405/K)
Divide both side by 6.28
1.49 / 6.28 = √(1405/K)
Take the square of both side
(1.49 / 6.28)² = 1405/K
2.2201 / 39.4384 = 1405/K
Cross multiply
2.2201 × K = 39.4384 × 1405
Divide both side by 2.2201
K = 39.4384 × 1405 / 2.2201
K = 24958.764 N/m
Thus, the spring constant is 24958.764 N/m