What would be ideal for dealing with a potential risk?

Let us take the position of mass when the spring is unstreched as $x = 0$, and the direction from left to right as the positive direction of x-axis. Give $x$ as a function of time $t$ for the oscillating mass if at the moment we start the stopwatch ($t = 0$), the mass is (a) at the mean position,

A circular disc of mass 10 kg is suspended by a wire attached to its centre. The wire is twisted by rotating the disc and released. The period of torsional oscillations is found to be 1.5 s. The radius of the disc is 15 cm. Determine the torsional spring constant of the wire. (Torsional spring constant $\alpha$ is defined by the relation $J = –\alpha \theta$, where $J$ is the restoring couple and $\theta$ the angle of twist).

Which of the following examples represent (nearly) simple harmonic motion and which represent periodic but not simple harmonic motion?
(d) general vibrations of a polyatomic molecule about its equilibrium position.

Fig. 14.23 depicts four x-t plots for linear motion of a particle. Which of the plots represent periodic motion? What is the period of motion (in case of periodic motion) ?

Answer the following questions :
(c) A man with a wristwatch on his hand falls from the top of a tower. Does the watch give correct time during the free fall ?

Which of the following functions of time represent (a) simple harmonic, (b) periodic but not simple harmonic, and (c) non-periodic motion? Give period for each case of periodic motion ($\omega$ is any positive constant):
(f) $1 + \omega t + \omega^2t^2$

A particle is in linear simple harmonic motion between two points, A and B, 10 cm apart. Take the direction from A to B as the positive direction and give the signs of velocity, acceleration and force on the particle when it is
(a) at the end A,

A body describes simple harmonic motion with an amplitude of 5 cm and a period of 0.2 s. Find the acceleration and velocity of the body when the displacement is
(b) 3 cm

Which of the following functions of time represent (a) simple harmonic, (b) periodic but not simple harmonic, and (c) non-periodic motion? Give period for each case of periodic motion ($\omega$ is any positive constant):
(a) $sin \omega t – cos \omega t$

Plot the corresponding reference circle for each of the following simple harmonic motions. Indicate the initial ($t =0$) position of the particle, the radius of the circle, and the angular speed of the rotating particle. For simplicity, the sense of rotation may be fixed to be anticlockwise in every case: ($x$ is in cm and $t$ is in s).
(d) $x = 2 cos \pi t$

Answer the following questions :
(b) The motion of a simple pendulum is approximately simple harmonic for small angle oscillations. For larger angles of oscillation, a more involved analysis shows that $T$ is greater than $2\pi \sqrt{\frac{l}{g}}$. Think of a qualitative argument to appreciate this result.

An upcoming RBI policy annoucement has made you think about whether not to trade in banking stocks just before the annoucement. What is your best strategy?

Answer the following questions :
(a) Time period of a particle in SHM depends on the force constant $k$ and mass $m$ of the particle: $T = 2\pi \sqrt{\frac{m}{k}}$. A simple pendulum executes SHM approximately. Why then is the time period of a pendulum independent of the mass of the pendulum?

An air chamber of volume $V$ has a neck area of cross section $a$ into which a ball of mass $m$ just fits and can move up and down without any friction (Fig.14.27). Show that when the ball is pressed down a little and released , it executes SHM. Obtain an expression for the time period of oscillations assuming pressure-volume variations of air to be isothermal [see Fig. 14.27].

A spring balance has a scale that reads from 0 to 50 kg. The length of the scale is 20 cm. A body suspended from this balance, when displaced and released, oscillates with a period of 0.6 s. What is the weight of the body ?

Between Index and Stocks, Index has a lower risk profile as a result of of risk diversification by the pool of underlying stocks 

A particle is in linear simple harmonic motion between two points, A and B, 10 cm apart. Take the direction from A to B as the positive direction and give the signs of velocity, acceleration and force on the particle when it is
(d) at 2 cm away from B going towards A,

When you're trying to exit a trade, the trading platform gives error messages. Turns out that the broker's servers are down. What kind of risk has just manifested itself?

If you're not 100% sure about a potential setup, which of these can you adopt to reduce risk?