Oscillations

Savitha, a XI standard student, while conducting an experiment to determine the effective length of a simple pendulum L, notes down the data of time taken to complete 30 oscillations as 60 s and hence calculates the length of the simple pendulum as : (Take π² = 9.8, and g = 9.8 m/s²)

The sum of kinetic energy and potential energy of a simple pendulum bob is 0.02 joule. The speed of the simple pendulum bob at equilibrium position is approximately : (Consider mass of the bob = 20 g)

The two-dimensional motion of a particle, described by $\overrightarrow{\mathrm{r}}=(\hat{i}+2\hat{j})\mathrm{Acos}\omega t$ is a/an:
A. parabolic path
B. elliptical path
C. periodic motion
D. simple harmonic motion

Choose the correct answer from the options given below :

If the mass of the bob in a simple pendulum is increased to thrice to its original mass and its length is made half its original length, then the new time period of oscillations $\frac{x}{2}$ times its original time period. Find the value of x:

The two-dimensional motion of a particle, described by $\overrightarrow{\mathrm{r}}=(\hat{i}+2\hat{j})\mathrm{Acos}\omega t$ is a/an:
A. parabolic path
B. elliptical path
C. periodic motion
D. simple harmonic motion

Choose the correct answer from the options given below :

[Re-NEET 2024]

A particle executing simple harmonic motion with amplitude A has the same potential and kinetic energies at the displacement :

[Re-NEET 2024]

If $x=5\sin \left(\pi t+\frac{\pi }{3}\right)m$ represents the motion of a particle executing simple harmonic motion, the amplitude and time period of motion, respectively, are :

[NEET 2024]