79.8k views
3 votes
Two springs having stiffness k1 and k2, respectively, are used in a vertical position to support a single object of mass m. Show that the angular frequency of oscillation is [(k1 + k2)/m]"2 if the springs are tied in parallel, and [k1k2/(k1 + k2)m]"2 if the springs are tied in series.Two springs having stiffness k1 and k2, respectively, are used in a vertical position to support a single object of mass m. Show that the angular frequency of oscillation is [(k1 + k2)/m]"2 if the springs are tied in parallel, and [k1k2/(k1 + k2)m]"2 if the springs are tied in series.

User CelineDion
by
6.6k points

1 Answer

3 votes

Answer:

Stiffness of spring 1 =K1

Stiffness of spring 2=K2

Mass =m

For parallel connection:

As we know that when spring are connects in parallel connection then equivalent stiffness given as


K=K_1+K_2

We know that natural frequency given as


\omega =\sqrt{(K)/(m)}

So


\omega =\sqrt{(K_1+K_2)/(m)}

For series connection:

As we know that when spring are connects in series connection then equivalent stiffness given as


(1)/(K)=(1)/(K_1)+(1)/(K_2)


K=(K_1K_2)/(K_1+K_2)

Now by putting values


\omega =\sqrt{(K)/(m)}


\omega =\sqrt{(K)/(m)}


\omega =\sqrt{(K_1K_2)/(m(K_1+K_2))}

User Bame
by
5.9k points