An object of mass m is attached to a horizontal spring, stretched to a displacement a from equilibrium and released, undergoing harmonic oscillations on a frictionless surface with period t0. the experiment is then repeated with a mass of 4m. the subsequent total mechanical energy of the object with mass 4m is which of the following when compared to the original total mechanical energy?
a. greater thanb. less thanc. equal to
matter that emits no light at any wavelength is called dark matter.
kinetic energy of any moving object = (1/2) (mass) (speed)²
jaylen's ke = (1/2) (54.6 kg) (15.1 m/s)²
ke = (27.3 kg) (228.01 m²/s²)
ke = 6,224.7 kg-m²/s²
ke = 6,224.7 joules
that may sound like a lot of ke. but jaylen's speed of 15.1 m/s is almost 50% faster than usain bolt's average speed for his world's record in the 100 meters, so you'd naturally expect amazingness from jaylen.
frequency determines the pitch we perceive. amplitude determines the volume, and loudness perceived (see more detail below)
a most fundamental wave shape is the sine (or cosine). a sine wave has three parameters: (1) frequency, (2) phase, and (3) amplitude. out of the three, two play a role in your question, as follows.
the frequency, namely the number of periods (repetitions) per second, is perceived by our ear of "the pitch." the higher the frequency, the higher the pitch. however, our ears perceive pitch as a logarithm of the physical frequency. every doubling of the frequency causes us to hear the pitch to increase by one octave.
the volume is determined by the amplitude of the wave. the higher the amplitude (positive or negative) the higher the volume. our ears perceive volume as "loudness" and, again, not linearly - some frequencies are perceived as louder than others, even though they have the same physical volume. frequencies between about 200 and 2000 hz are perceived as louder than the rest of the audible spectrum (between 20 and 20000 hz).
interestingly, the phase does not play all too prominent role in perception, at least as far as music and speech are concerned.
-- "declination zero" means the object is in the sky at some point directly over the earth's equator.
-- if it's the sun and it appears to be over the equator, then that tells us that the earth's axis is not tilted toward or away from it.
-- that in turn tells us that the earth is at one of the two equinoxes in its orbit, either the spring one or the autumn one. (d)
-- (the first days of summer and winter coincide with solstices, not equinoxes.)