## Question

Which of the following equations represents a simple harmonic motion? The displacement of the system from the equilibrium position is *x* at time *t*and α is a positive constant.

### Solution

In a simple harmonic motion, the acceleration *d*^{2}*x*/*dt*^{2} must be proportional to the displacement *x* and opposite to it, i.e., where α is a positive constant.

#### SIMILAR QUESTIONS

Nine tuning forks are arranged in order of increasing frequency. Each tuning fork produces 4 beats per second when sounded with either of its neighbours. If the frequency of the 9^{th} tuning fork is twice that of the first, what is the frequency of the first tuning fork?

Figure shows the displacement-time graphs of two simple harmonic motions I and II. From the graphs it follows that the two motion I and II have

What is the phase difference between the two simple harmonic motions whose displacement-time graphs are shown in figure?

The displacement *x* (in metres) of a particle in simple harmonic motion is related to time *t* (in seconds) as

What is the frequency of the motion?

A simple pendulum of frequency *n* is taken up to a certain height above the ground and then dropped along with its support so that it falls freely under gravity. The frequency of oscillations of the falling pendulum will

A person measures the time period of a simple pendulum inside a stationary lift and finds it to be T. If the lift starts accelerating upwards with an acceleration of g/3, the time period of the pendulum will be

The length of a simple pendulum is increased by 44%. What is the percentage increase in its time period?

A hollow metallic sphere filled with water is hung from a support by a long thread. A small hole is made at the bottom of the sphere and it is oscillated. How will the time period of oscillations be affected as water slowly flows out of the hole?

A simple pendulum with a brass bob has a time period *T*. The bob is now immersed in a non-viscous liquid and oscillated. If the density of the liquid is 1/8 that of brass, the time period of the same pendulum will be