Physics · Oscillations · NEET
No, and this is the most common mix-up. Frequency f is oscillations per second (unit Hz). Angular frequency omega is radians per second (unit rad/s). They are linked by omega = 2 pi f. So omega is about 6.28 times bigger than f. When a NEET equation gives you omega, divide by 2 pi to get f, or use T = 2 pi / omega directly for the period.
Look only at the number multiplying t inside the sine. That number is omega (angular frequency) in rad/s. Then T = 2 pi / omega. Example: x = 5 sin(pi t + pi/3), here omega = pi, so T = 2 pi / pi = 2 s. The amplitude is the number in front (5), and the phase constant pi/3 does NOT change the period.
Time period T is measured in seconds (s) because it is a time. Frequency f is measured in hertz (Hz), which means per second (1/s). A frequency of 5 Hz means 5 oscillations every second, so each oscillation takes T = 1/5 = 0.2 s. Never write T in Hz or f in seconds.
Time period is total time divided by number of oscillations: T = 60 / 30 = 2 s. Frequency is number of oscillations divided by total time: f = 30 / 60 = 0.5 Hz. Check: T = 1/f = 1/0.5 = 2 s. This is a very common NEET-style step, often hidden inside a pendulum-length question.
No. For SHM (like a pendulum or spring-mass), the time period and frequency depend on the system (length, mass, spring constant, g) but NOT on how far you pull it. A bigger amplitude means the body moves faster but covers more distance, so the time for one swing stays the same. This is called isochronism.
If x = 5 sin(pi t + pi/3) m represents the motion of a particle executing simple harmonic motion, then the amplitude and time period of the motion, respectively, are
Savitha, a Class XI student, records the time for 30 oscillations of a simple pendulum as 60 s. The length she calculates is (take pi squared = 9.8 and g = 9.8 m/s^2)
Try the real previous-year questions from this chapter — each with the answer and a full solution.
T = 1/f and f = 1/T. Time period T is in seconds, frequency f is in hertz. They are reciprocals of each other.
omega = 2 pi f, and also omega = 2 pi / T. So angular frequency is 2 pi times the ordinary frequency. To go from omega to T, use T = 2 pi / omega.
The SI unit of frequency is the hertz (Hz), which equals one oscillation per second (1/s). Time period has the unit second (s).
Yes. 1 Hz means the body completes exactly one full oscillation every second, so its time period is 1 s.
Yes. Amplitude and time period are independent. A spring-mass and a pendulum can be released with the same amplitude yet have different periods because their periods depend on k, m, L and g, not on amplitude.
