# Problems on SHM of Springs

Physics

## example

### Solve problems on describing motion of two blocks attached with a spring

Example: A block of mass placed on top of another block of mass is attached to a horizontal spring of force constant as shown in figure. The coefficient of friction between the blocks is where as the lower block slides on a friction less surface. The amplitude oscillation is 0.4 m. What is the minimum value of such that the upper block does not slip over the lower block?
The upper block does not slip over the lower block when the restoring force is balanced by the friction force of lower block against ground. i.e,
or

## example

### Problem of various combination of Springs

Let the spring constant of the spring be .
Thus the effective spring constant of the parallel combination as shown in the figure=
Thus in a series combination of above springs, effective spring constant=
In parallel combination of above springs, effective spring constant=
Thus

## example

### Solve problems in which part of the motion is SHM

Equivalent spring constant:

## example

### SHM in spring in accelerated frame of reference

Example:
A block of mass kg is kept on smooth floor of a truck. One end of a spring of force constant N/m is attached to the block and other end is attached to the body of truck as shown in the figure. At , truck begins to move with constant acceleration m/s. Find the amplitude of oscillation of block relative to the floor of truck.
Solution:
Let is the compression in equilibrium. Then

m
Amplitude
m

## example

### Springs in rotational SHM

Example:
A uniform rod of length l mass m is fixed at the centre. A spring of spring constant k is connected  to rod and wall as shown in figure. The rod is displaced by small angle and released. Find time period of oscillation.
Solution:
Let the length of the rod be .
Torque acting on the rod about the center of the rod is given by