Development of Dynamics; XXV.
This gives the physical significance of the constant A. It is the maximum displacement of the particle from the center of oscillation i.
To describe the motion quantitatively, a particular instant should be called zero and measurement of time should be made from this instant.
We know that the motion repeats after a certain time called the time period T of the motion i. Velocity The expression for velocity can be derived by differentiating the displacement w.
When the magnitude of displacement is least, that of the velocity is maximum and vice versa. Acceleration Knowing the velocity we can arrive at acceleration for simple harmonic motion by differentiating the velocity, i. Also the acceleration curve is shifted to the left by 90o w.
Simple Pendulum A simple pendulum consists of a heavy particle suspended from a fixed support through a light, inextensible string.
This system can stay in equilibrium if the string is vertical. This is called the mean position or the equilibrium position. The torque of T is zero as it intersects OA at point O. Physical Pendulum Any rigid body suspended from a fixed support constitutes a physical pendulum.
The motion of such a system can be followed very nearly in the same way as that of a simple pendulum. The distance of the center of mass of the body from the fixed suspension point acts as the effective length of the pendulum and the total mass being the mass of the particle situated at the center of the body.
This system can now be treated in exactly the same way as a simple pendulum. The body is rotated about the wire as the axis of rotation. The twisted wire exerts a restoring torque on the body to bring it back to its original position i. The damping force is a function of speed and is directed opposite to the velocity.
Energy is lost due to the negative work done by the damping force and the system comes to a halt in due course.An article on the history and theories of physics. Linear motion (also called rectilinear motion) is a one-dimensional motion along a straight line, and can therefore be described mathematically using only one spatial heartoftexashop.com linear motion can be of two types: uniform linear motion with constant velocity or zero acceleration; non uniform linear motion with variable velocity or non-zero acceleration.
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