How To Solve Equations Of Simple Harmonic Motion Effectively For JEE Exam?
As we know that cracking JEE exam is the most crucial aspect and dream of many aspiring engineering students. JEE is one of the ideal ways to get into the top renowned colleges of India. Physics is a logical and concept based subject that demands high attention and application level knowledge to solve the questions. Out of many topics, students feel it is tricky to solve the equations from Simple Harmonic Motion and Wave motion. Problem-solving in physics is a difficult task for students to understand and faculties to teach. Some students get it easily, while others struggle.
Let us explain Simple Harmonic Motion (SHM)
Simple Harmonic Motion (SHM) is defined as the motion which is repetitive and periodic in nature. In other words, SHM is defined as a motion in which the restoring force is directly proportional to the displacement of the body from its mean position. SHM is seen in a repetitive motion back and forth about an equilibrium position.
In SHM, this site is periodic and sinusoidal in nature.
Example: It is observed in the motion of the pendulum, vibration of musical instruments and sound waves.
Simple Harmonic Motion is classified into two types
● Linear SHM
● Angular SHM
Important Concepts & Formulas On SHM
Spring-based problems using force method
1. Analyze the situation carefully and understand the given problem
2. Do not attempt the problem until you understand the question
3. First, displace the object from the equilibrium position
4. Find all the forces or torque that are applied to the object.
5. Build a relationship between displacement and restoring the force
6. Find the angular frequency formula
Consider the spring in two conditions, as shown in the figure below.
Consider a spring attached to the body of mass m. k= spring constant.
The body is displaced by some position. Determine the force acting at point t at location x. The force acting on the object is referred to as restoring force.
Restoring force is given by kx.
Hence,
F= – kx
The negative sign represents the force acting in the opposite direction.
k = force constant.
SI unit = N/m.
Hence,
To find energy with respect to time
To find total energy at point t. You need to consider the energy stored in the spring + Kinetic energy of the object.
Applying differentiation on both sides
Or
Solve energy based SHM problems
1. Read and understand the problem carefully
2. Do not attempt the problem until you understand the question
3. Check every energy component of the system with respect to t.
4. Know that angular velocity is expressed in the form of linear velocity using v = rω
5. Know the general SHM motion equation
Consider a solid cylinder of Radius R and Mass M attached to one end of the spring. Spring constant = K. The cylinder is considered to roll without slipping off the floor. The cylinder is moving away from the equilibrium position and then left. Time taken = t, the spring is stretched by x and moving with velocity v is as shown in the figure below.
The Spring Potential energy is given by
Cylinder Kinetic energy is given by
Cylinder Rotational energy given by
Inertia is given by (when cylinder rolls without slipping off)
Angular velocity is given by
ω=v/R
Rotational energy is given by
The total energy is given by
Differentiating both sides and considering dE/dt=0
Hence, angular frequency is given by
Try to apply and remember these formulas to crack any competitive examinations. JEE will have more preference and weightage to SHM based problems. Hence give more importance to this concept.
For more information on Simple Harmonic motion, refer BYJU’S! Also, explore more important topics on BYJU’S YouTube channel.
