A rectangular cantilever aluminium beam has first natural frequency ω rad/s. If length doubles with material and cross section unchanged, its first frequency becomes
For an Euler–Bernoulli cantilever, $\omega_1=\beta_1^2\sqrt{EI/(\rho A)}/L^2$, with unchanged dimensionless mode constant β₁. Doubling L multiplies frequency by 1/4, so A.
More Structural dynamics: free and forced vibration of SDOF systems and free vibration of 2-DOF systems questions
GATE 2020 AE Q61– A critically damped door-closing spring–mass–damper becomes overdamped as its spring…
GATE 2020 AE Q62– The two-degree-of-freedom system shown has initial displacements x₁ = 2 cm and x₂ = 1.24…
GATE 2019 AE Q35– In the spring–mass system shown, m=3 kg and each spring has stiffness k=20 kN/m. Find the…
GATE 2019 AE Q64– A damped spring–mass system has m=10 kg, stiffness 1000 N/m and damping coefficient 20 N…
GATE 2019 AE Q65– Two masses of 10 kg each are connected between fixed supports by outer springs of…
GATE 2024 AE Q14– Consider the free vibration responses P, Q, R and S (shown in the figure) of a single…