Oscillations Of A Spring-mass System - Practice Questions & MCQ

Spring Force:-

• Spring force is also called restoring force.

•  

           where k is the spring constant and its unit is N/m and x is net elongation or compression in the spring.

           Spring constant (k) is a measure of stiffness or softness of the spring

• Here -ve sign is because the force exerted by the spring is always in the opposite direction to the displacement. 

The time period of the Spring mass system-

1. Oscillation of a spring in a verticle plane-

Finding Time period of spring using Force method.

Let   be the deformation in the spring in equilibrium. Then  When the block is further displaced by x , the net restoring force is given by  as shown in the below figure.

using   and 

we get 

comparing it with the equation of SHM i.e 

we get 

similarly 

2.Oscillation of spring in the horizontal  plane

For the above figure, Using force method we get a Time period of spring as  and  

• Key points

      1. The time period of a spring-mass system  depends on the mass suspended  

                

     2.  The time period of a spring-mass system depends on the force constant k of the spring 

           

   3. The time period of a spring-mass system is independent of acceleration due to gravity.

  4. The spring constant k is inversely proportional to the spring length.

    

i.e 

That means if the length of spring is halved then its force constant becomes double.

  5.  When a spring of length l is cut in two pieces of length l₁ and l₂ such that  

     So using

 

 If the constant of a spring is k then

using 

i.e 

we get

  

   6.  If the spring has a mass M and mass m is suspended from it, then its effective mass is given by 

     and 

 

 

 

 

1. Series combination of spring

If 2 springs of different force constant are connected in series as shown in the below figure

then k=equivalent force constant is given by 

Where  are spring constants of spring 1 & 2 respectively.

Similarly, If n springs of different force constant are connected in series having force constant  respectively

then 

If all the n spring have the same spring constant as  then   

2.The parallel combination of spring

If 2 springs of different force constant are connected in parallel as shown in the below figure

       

then k=equivalent force constant is given by 

where  are spring constants of spring 1 & 2 respectively.

Similarly, If n springs of different force constant are connected in parallel having force constant  respectively

then 

If all the n spring have the same spring constant as  then