A metal rod of length 1m is clamped at two points as shown in the figure. Distance of the clamp from the two ends are 5 cm and 15 cm, respectively. Find the minimum and next higher frequency of natural longitudinal oscillation of the rod. Given that Young's modulus of elasticity and density of aluminium are `Y= 1.6 xx 10^(11) Nm^(-2)` and `rho = 2500 kgm^-3` , respectively.

A suructural steel rod has a radius of 10mm and a length of 1m. A 100 kN force stretches it along its length. Calculate (a) the stress (b) elongation, and (c ) percentage strain on the rod. Given that the Young's modulus of elasticity of structural steel is 2.0 xx 10^(11) Nm^(-2) .

A metallic rod of length 1m has one end free and other end rigidly clamped. Longitudinal stationary waves are set up in the rod in such a way that there are total six antinodes present along the rod. The amplitude of an antinode is 4 xx 10^(-6) m . young's modulus and density of the rod are 6.4 xx 10^(10) N//m^(2) and 4 xx 10^(3) Kg//m^(3) respectively. Consider the free end to be at origin and at t=0 particles at free end are at positive extreme. The magnitude of strain at midpoint of the rod at t = 1 sec is

A metallic rod of length 1m has one end free and other end rigidly clamped. Longitudinal stationary waves are set up in the rod in such a way that there are total six antinodes present along the rod. The amplitude of an antinode is 4 xx 10^(-6) m . young's modulus and density of the rod are 6.4 xx 10^(10) N//m^(2) and 4 xx 10^(3) Kg//m^(3) respectively. Consider the free end to be at origin and at t=0 particles at free end are at positive extreme. The equation describing stress developed in the rod is

A metallic rod of length 1m has one end free and other end rigidly clamped. Longitudinal stationary waves are set up in the rod in such a way that there are total six antinodes present along the rod. The amplitude of an antinode is 4 xx 10^(-6) m . young's modulus and density of the rod are 6.4 xx 10^(10) N//m^(2) and 4 xx 10^(3) Kg//m^(3) respectively. Consider the free end to be at origin and at t=0 particles at free end are at positive extreme. The equation describing displacements of particles about their mean positions is.

A ligh rod of length 1 m is pivoted at its centre and two masses of 5 kg and 2 kg are hung from the ends as shown in the figure. Find the initial angular acceleration of the rod assuming that it was horizontal in the beginning.

A closed orgain pipe of length l_(0) is resonating in 5^(th) harmonic mode with rod clamped at two points l and 3l from one end. If the length of the rod is 4l and it is vibrating in first overtone. Find the length of the rod. [Velocity of sound in air =v_(s) Young's modulus for the rod Y and density rho ]

A wire of density 9000 kg//m^(3) is stretched between two clamps 100 cm apart while subjected to an extension od 0.05 cm . What is the lowest frequency of transverse vibrations in the wire , assuming Young's modulus of the material to be 9 xx 10^(10) N//m^(2) ?