big, dramatic, huge, sharp, violent, wide (esp. AmE)
violent swings in policy

small
10%, etc.
sudden, wild
his sudden swings of mood

electoral, national (esp. BrE)
mood
She suffers from severe mood swings.

need
The party needs a swing of only 2.5% to win.

represent
This represents a swing of 14% against the party.

suffer, suffer from

state, vote, voter (all esp. AmE)
Ohio is a swing state in the presidential election.

swing in favour of (BrE), swing to, swing towards/toward
signs of a late swing to the Democrats

swing against
a dramatic swing against the socialists

swing away from
the swing away from science in schools

swing from
swing in
a sharp swing in the attitudes of economists

wild
mighty (esp. AmE), powerful
backward, forward
golf
practice

do, make, take
the technique for making the perfect golf swing

change
practise/practice
The golfers were practising/practicing their swings.

bridge, door (both BrE)

swing at
He took a wild swing at the ball.

swing of
There was a political swing of the pendulum back to the right. (figurative)

porch, tyre/tire (both esp. AmE)

go on, play on, sit on
Some kids were playing on the swings.

on a/the swing
Her dad pushed her on the swing.

gently, slowly
violently, wildly
She lashed out, her arm swinging wildly.

freely
Let your arms swing freely at your sides.

back and forth, from side to side, to and fro
The pendulum swung slowly from side to side.

from
I could see him swinging from the branch of a large tree.

slowly
suddenly
sharply
The road swung sharply around.

across, around, away, back, down, forward, off, round (esp. BrE), up
Hearing a sarcastic note in his voice, she swung around to face him.

let sth
She let the door swing shut behind her.

from
She swung down from the tree in one easy movement.

into
He swung up into the saddle and rode off.

towards/toward
Nick swung towards/toward her.

swing open, swing shut

rapidly
suddenly
wildly
The balance of power swung wildly from one party to the other.

heavily
Opinion swung heavily to the left.

from, to
Her mood could swing rapidly from gloom to exhilaration.

Swing is used with these nouns as the subject:
arm, bag, balance, batter, hip, leg, monkey, price

Swing is used with these nouns as the object:
arm, axe, backpack, bag, balance, basket, bat, baton, blade, deal, election, fist, foot, hammer, handbag, head, hip, leg, punch, racket, vote