You stretch a spring by a distance of 0.05 m. the spring has a spring constant of 125 n/m. when you release the spring, it snaps back. what is the kinetic energy of the spring as it reaches its natural length?

What would the difference of spectral lines emitted by hydrogen gas in distant galaxies which is normally found at a wavelength of 21 cm on earth, be observed at 21.1 centimeters?

The frequency of vibrations of a vibrating violin string is given by f = 1 2l t ρ where l is the length of the string, t is its tension, and ρ is its linear density.† (a) find the rate of change of the frequency with respect to the following. (i) the length (when t and ρ are constant) (ii) the tension (when l and ρ are constant) (iii) the linear density (when l and t are constant) (b) the pitch of a note (how high or low the note sounds) is determined by the frequency f. (the higher the frequency, the higher the pitch.) use the signs of the derivatives in part (a) to determine what happens to the pitch of a note for the following. (i) when the effective length of a string is decreased by placing a finger on the string so a shorter portion of the string vibrates df dl 0 and l is ⇒ f is ⇒ (ii) when the tension is increased by turning a tuning peg df dt 0 and t is ⇒ f is ⇒ (iii) when the linear density is increased by switching to another string df dρ 0 and ρ is ⇒ f is ⇒

The frequencies refer to the sample data collected from a population of interest when performing a hypothesis test comparing two or more population proportions.