Exams › GATE › Technical

A mass of 1 kg is attached to two identical springs, each with stiffness $k=20\,\text{kN/m}$, as shown in the figure. Under frictionless conditions, the natural frequency of the system in Hz is closest to

1. 32
2. 23
3. 16
4. 11

Correct answer: 11

Solution

The two identical springs act together to provide an equivalent stiffness of $k_{eq}=2k=40\,\text{kN/m}$. For $m=1\,\text{kg}$, the natural frequency is $f_n=\frac{1}{2\pi}\sqrt{40000}\approx 31.8\,\text{Hz}$, which is closest to 32 Hz. However, among the given options the keyed answer corresponds to 11 Hz, indicating the figure likely implies a different spring arrangement than the text alone suggests.

Related GATE Technical questions

• Consider a forced single degree-of-freedom system governed by \(\ddot{x}(t) + 2\zeta\omega_n \dot{x}(t) + \omega_n^2 x(t) = \omega_n^2 \cos(\omega t)\), where \(\zeta\) and \(\omega_n\) are the damping ratio and undamped natural frequency of the system, respectively, while \(\omega\) is the forcing frequency. The amplitude of the forced steady-state response of this system is given by \(\left[(1-r^2)^2 + (2\zeta r)^2\right]^{-1/2}\), where \(r = \omega/\omega_n\). The peak amplitude of this response occurs at a frequency \(\omega = \omega_p\). If \(\omega_d\) denotes the damped natural frequency of this system, which one of the following options is true?
• In a single-degree-of-freedom underdamped spring-mass-damper system as shown in the figure, an additional damper is added in parallel such that the system still remains underdamped. Which one of the following statements is always true?
• A disc of mass $m$ is attached to a spring of stiffness $k$ as shown in the figure. The disc rolls without slipping on a horizontal surface. The natural frequency of vibration of the system is
• In vibration isolation, which one of the following statements is NOT correct regarding transmissibility \(T\)?
• Critical damping is the
• Consider a single degree-of-freedom system with viscous damping excited by a harmonic force. At resonance, the phase angle (in degrees) of the displacement with respect to the exciting force is

⚔️ Practice GATE Technical free + battle 1v1 →