GATE Overflow for GATE XE - Questions without answers in Vibrations

GATE XE 2025 | Question: 71

Sun, 04 May 2025 19:06:41 +0000

The natural frequency of a spring-mass system is $10 \: \mathrm{rad} / \mathrm{s}$.

Which of the following statements is/are $\textsf{CORRECT}$?

The mass is $100 \:\mathrm{kg}$ and the stiffness is $1 \mathrm{~N} / \mathrm{m}$.
The mass is $1.25 \: \mathrm{kg}$ and the stiffness is $125 \mathrm{~N} / \mathrm{m}$.
The stiffness is $620 \mathrm{~N} / \mathrm{m}$ and the mass is $6.2 \:\mathrm{kg}$.
The stiffness is $62 \mathrm{~N} / \mathrm{m}$ and the mass is $620 \mathrm{kg}$ .

GATE XE 2025 | Question: 85

Sun, 04 May 2025 19:06:12 +0000

A massless cantilever beam, with a tip mass m of $10 \: \mathrm{kg}$, is modeled as an equivalent spring-mass system as shown in the figure. The beam is of length $\mathrm{L}=1 \mathrm{~m}$, with a circular cross-section of diameter $\mathrm{d}=20 \mathrm{~mm}$. The Young's modulus of the beam material is $200 \: \mathrm{GPa}$.

The natural frequency of the spring-mass system is $\_\_\_\_\_\_\_ \: \mathrm{Hz}$ (rounded off to two decimal places).