the displacement of particle in simple harmonic motion is
maaz , 7 Years ago
Grade 12th pass
Mechanics> the displacement of particle in simple ha...
1 AnswersVikas TU
Last Activity: 7 Years ago
Consider any molecule executing SHM with birthplace as it's balance position affected by reestablishing power F=kx , where k - compel steady and x = removal of molecule from the balance position.
Presently since F= - kx is the reestablishing power and from Newton's law of movement compel is give as F=ma , where m is the mass of the molecule moving with quickening a. Along these lines quickening of the molecule is
a=F/m
=-kx/m
in any case, we realize that increasing speed a=dv/dt=d2x/dt2
⇒ d2x/dt2=-kx/m (1)
This condition 1 is the condition of movement of SHM.
On the off chance that we pick a consistent φ=√(k/m) at that point condition 1 would progress toward becoming
d2x/dt2=-φ2x (2)
This condition is a differential condition which says that dislodging x must be an element of time with the end goal that when it's second subordinate is figured the outcome must be negative consistent duplicated by the first capacity.
Sine and cosine capacities are the capacities fulfilling above necessity and are recorded as takes after
x=A sinωt (3a)
x=A cosωt (3b)
x=A cos(ωt+φ) (3c)
every one of condition 3a, 3b and 3c can be submitted on the left hand side of condition 2 and can then be explained for confirmation.
Advantageously we pick condition 3c i.e., cosine shape for speaking to removal of molecule whenever t from balance position. Hence,
x=A cos(ωt+φ) (4)
also, A , φ and φ are all constants.
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