Find expression for the various harmonics in a vibration string fixed at the two ends.Hence predict the position of nodes and antinodes.

The pattern of standing waves formed on a stretched string at two instants of time are shown in the figure.The velocity of two waves superimposing to form stationary waves in 360ms^(-1) and their frequencies are 256 Hz. Mark nodes and antinodes on the curve.

In many experimental set-ups, the source and screen are fixed at a distance say D and the lens is movable.Show that there are two positions for the lens,for which an image is formed on the sceen.Find the distance between these points and the ratio of the image sizes for these two points.

Two masses 8 kg and 12 kg are connected at the two ends of a light inextensible string that goes over a frictionless pulley. Find the acceleration of the masses, and the tension in the string when the masses are released.

If veca,vecb,vecc are the position vectors of the vertices A,B,C of a /_\ABC respectively, find an expression for the area of /_\ABC and hence deduce the condition for the points A,B,C to be collinear.

Two bodies of masses m_1 and m_2 are connected byh a ight string passing over a smooth light pulley fixed at the end of an inclined plane.the mass m_1 lies on the inclined plne nd m_2 bags vertically.The system is at rest.Find the angle of the inclination of the inclined plane and the force exerted by the inclined plane on the body of mass m_1 .

A point particle of mass M is attached to one end of a massless rigid non-conducting rod of length L. Another point particle of the same mass is attached to the other end of the rod. The two particles carry charges +q and -q respectively. This arrangement is held in a region of a uniform electric field E such that the rod makes a small angle theta (say of about 5 degree) with the field direction, fig. Find an expression for the minimum time needed for the rod to become parrallel to the field after it is set free.

A body of mass m is attached to one end of a massless spring which is suspended vertically from a fixed point. The mass is held in hand so that the spring is neither stretched nor compressed. Suddenly the support of the hand is removed. The lowest position attained by the mass during oscillation is 4 cm below the point, where it held in hand. Find the frequency of oscillation?

Show that when a string fixed at two ends vibrates in 1 loops,2 loops,3 loops and 4 loops, the frequencies are in the ratio 1:2:3:4.