A mass of 1 kg is suspended by means of 3 springs as shown

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A mass of 1 kg is suspended by means of 3 springs as shown in figure. The spring constant K₁, K₂ and K₃ are respectively 1 kN/m, 3 kN/m and 2 kN/m. The natural frequency of the system is approximately

1. 46.90 rad/s
2. 52.44 rad/s
3. 60.55 rad/s
4. 77.46 rad/s

Correct Option: B

K₁ and K₂ are in series,

∴	1	=	1	+	1	=	1	+	1	=	4
	K_eq1		K₁		K₂		1		3		3

K_eq1 and K₃ are in parallel arrangement,

K_eq = K_eq1 + K₃ =	3	+ 2 =	11	kN / m
	4		4

Natural frequency, ω = √K_eq / m = √(11 × 10³) / (4 × 1) = 52.44 rad / s