Class 11th

Resonance occurs when the frequency of an external periodic force matches the natural frequency of a system. From that, physicists know that resonance causes the amplitude of oscillations to increase significantly. This can be beneficial in devices, such as musical instruments, but dangerous in structures like bridges.

The phase in SHM tells us the position and direction of motion of the particle at a specific instant. It determines the state of oscillation and includes both displacement and time information.

The restoring force in SHM is the force that always acts towards the mean position and is directly proportional to the displacement from it. It follows F=? kx. Here, the negative sign indicates the force is in the opposite direction to the displacement.

Sol. Before collision $\Rightarrow$

It undergoes completely inelastic collision

Using conservation of linear momentum

Initial momentum = Final momentum

$\Rightarrow m{v}_1=m{v}_2+m{v}_2$

$\Rightarrow m{v}_1=2m{v}_2$

$\Rightarrow \frac{v_1}{v_2}=\frac{2}{1}$

$x=2t-1$

$v=\frac{dx}{dt}=2 m s^{-1}$

$P=F·v$

$=2*5=10 W$

In the case of pure rolling,

The topmost point will have velocity $2v$ while point $Q$ i.e. the lowest point will have zero velocity. Hence point $P$ moves faster than point $Q$ .

Air resistance resists the motion of an object. In this case, the net acceleration is lesser than 'g' and it shrinks as the speed increases. This makes the object to speed up more slowly. Ultimately, it reaches a constant terminal velocity which is lower for large-area ones and higher for heavy and streamlined ones.

Suppose the position-time graph is a straight line, in this case, the velocity is constant. This means that there is no acceleration.
If the graph is curved, velocity is changing, which means that there is acceleration. If the graph is concave, the slopes will get more positive with time. This means that there is positive acceleration. If the graph is cap-shaped, the slope will become more negative with time. This is known as negative acceleration.

To graph motion in a straight line, you need to visualise the relationship between different kinematic quantities like position, velocity and time. Suppose an object moves with a constant velocity, the position-time graph will be a straight line with constant slope. If the object accelerates, the slope of position-time graph will change with time and result in a curved line.

No. Since kinetic energy is a scalar quantity, it only depends on speed of the body and not the direction. So if the direction of the body is changed but the speed remains unchanged, there won't be any effect on the kinetic energy. However, if changing the direction also changes the speed of the body, then kinetic energy of the body will also change.