Question

Use your definition to explain how simple harmonic motion can be represented by the equation y = a sin ωt

(a) Show that the above equation is dimensionally correct

Answer 1

Y = a sin ωt

sin ωt has no dimensions. Hence we get L = L

Hence this equation is dimensionaly correct.

Base quantity	S.I units
	Name	symbol	definition
Length	meter	m	The meter is the length of the path travelled by light in vacuum during a time interval of 1/299.792.458 of the second.(1983)
Mass	Kilogram	Kg	The kilogram is equal to the mass of the international prototype of the kilogram (a  platinum- iridium alloy cylinder) kept at international bureau of weight and Measures at serves, near paris, France.(1889)
Time	Second	s	The second is the during of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom. (1967)
Electric current	ampere	A	The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 meter apart in vacuum. would produce between these conductors a  force equal to 2 x 10-7 newton per meter of length.(1948)
Thermo- dynamic temperature	kelvin	K	The kelvin, is the fraction 1/273.16 of the thermodynamic temperature of the  triple point of water.(1967)
Amount of substance	mole	mol	the mol is the amount of substance of a system, which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon-12. (1971)
Luminious	Candela	cd	the candela is the luminous intensity, in a given