simple harmonic motion class 10 | mass attached to spring class 10 | 10th class physics chapter 10
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simple harmonic motion class 10 | mass attached to spring class 10 | 10th class physics chapter 10
A body is said to be vibrating if it moves back and forth or to
and fro about a point. Another term for vibration is
oscillation. A special kind of vibratory or oscillatory motion is
called the simple harmonic motion (SHM), which is the main
focus of this chapter. We will discuss important
characteristics of SHM and systems executing SHM. We will
also introduce different types of waves and will demonstrate
their properties with the help of ripple tank.
10.1 SIMPLE HARMONIC MOTION (SHM)
In the following sections we will discuss simple harmonic
motion of different systems. The motion of mass attached to
a spring on a horizontal frictionless surface, the motion of a
ball placed in a bowl and the motion of a bob attached to a
string are examples of SHM.
MOTION OF MASS ATTACHED TO A SPRING
One of the simplest types of oscillatory motion is that of
horizontal mass-spring system (Fig.10.1). If the spring is
stretched or compressed through a small displacement x
from its mean position, it exerts a force F on the mass.
According to Hooke’s law this force is directly proportional to
the change in length x of the spring i.e.,
........ (10.1)
where x is the displacement of the mass from its mean
position O, and k is a constant called the spring constant
defined as
The value of k is a measure of the stiffness of the spring. Stiff
springs have large value of k and soft springs have small value
of k.
It means that the acceleration of a mass attached to a spring
is directly proportional to its displacement from the mean
position. Hence, the horizontal motion of a mass-spring
system is an example of simple harmonic motion.
For your information
A spider detects its prey due to
vibration produced in the web.
2
SIMPLE HARMONIC MOTION AND WAVES
........ (10.2)
The negative sign in Eq. 10.1 means that the force exerted by
the spring is always directed opposite to the displacement of
the mass. Because the spring force always acts towards the
mean position, it is sometimes called a restoring force.
A restoring force always pushes or pulls the object performing
oscillatory motion towards the mean position.
Initially the mass m is at rest in position O and the
mean
resultant force on the mass is zero (Fig.10.1-a). Suppose
the mass is pulled through a distance x up to extreme
position A and then released (Fig.10.1-b). The restoring
force exerted by the spring on the mass will pull it
towards the position O. Due to the restoring force
mean
the mass moves back, towards the mean position O. The
magnitude of the restoring force decreases with the
distance from the mean position and becomes zero at O.
However, the mass gains speed as it moves towards the
mean position and its speed becomes maximum at O.
Due to inertia the mass does not stop at the mean
position O but continues its
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