A Simple Pendulum Of Bob Mass m is Oscillating With An Angular Amplitudeαm (in Radius). The Maximum Tension In The String Is

Two springs of force constants k₁ and k₂ are connected to a mass mplaced on a horizontal frictionless surface as shown in fig (a) and (b). What is the ratio of the time periods of horizontal oscillation in cases (a) and (b) if k₁ = k₂?

Two springs of force constants k₁ and k₂ are connected to a mass m as shown in fig (a) and (b). What is the ratio of the time periods of vertical oscillation in cases (a) and (b) if k₁ = k₂?

A tray of mass M = 10 kg is supported on two identical springs, each of spring constant k, as shown in fig. When the tray is depressed a little and released, it executes simple harmonic motion of period 1.5 s. When a block of mass m is placed on the tray, the period of oscillation becomes 3.0 s. The value of m is  

A vertical U-tube of uniform cross-sectional area A contains a liquid of density ρ. The total length of the liquid column in the tube is L. The liquid column is disturbed by gently blowing into the tube. If viscous effects are neglected, the time period of the resulting oscillation of the liquid column is given by 

A cylindrical piece of cork of height h and density ρ_c floats vertically in a liquid of density ρ_l. The cork is depressed slightly an released. If viscous effects are neglected, the time period of vertical oscillations of the cylinder is given by

An air chamber of volume V has a neck of cross-sectional area a into which a light ball of mass m can move without friction. The diameter of the ball is equal to that of the neck of the chamber. The ball is pressed down a little and released. If the bulk modulus of air in B, the time period of the resulting oscillation of the ball is given by 

A simple pendulum of length l and bob mass m is displaced from its equilibrium position O to a position P so that the height of P above O is h. It is then released. What is the tension in the string when the bob passes through the equilibrium position O? Neglect friction. V is the velocity of the bob at O.

A trolley of mass m is connected to two identical springs, each of force constant k, as shown in fig. The trolley is displaced from its equilibrium position by a distance x and released. The trolley executes simple harmonic motion of period T. After some time it comes to rest due to friction. The total energy dissipated as heat is (assume the damping force to be weak)

Figure (a) shows a spring of force constant k fixed at one end and carrying a mass m at the other end placed on a horizontal frictionless surface. The spring is stretched by a force F. figure (b) shows the same spring with both ends free and a mass m fixed at each free end. Each of the spring is stretched by the same force F. the mass is case (a) and the masses in case (b) are then released.

Which of the following statements is/are true? 

A particle is executing simple harmonic motion. Its displacement is given by   

where x is in cm and t in seconds. How long will the particle take to move from the position of equilibrium to the position of maximum displacement?